Not really, unless you're willing to allow a lot of stretches and assumptions.
We could scrape a motivation for Arata to have ordered the abduction.
Firstly, it could be argued he had the motive: he has asked Rumata multiple times for "lightnings", to crush the oppressors of common folk. Rumata always refused, justifying the refusal by the very possible scenario where one of Arata's old allies would overthrow him and use the "lightnings" for less noble purposes.
“No,” said Rumata, “I will not give you lightning. It would be a mistake. Try to believe me. I can see further than you.” Arata was listening, his head sunk on his chest. Rumata clenched his hand. “I will only give you one reason. It pales in comparison with the primary reason, but you will actually understand it. You are very good at surviving, worthy Arata, but you too are mortal; and if you die, if the lightning passes into other hands that are not as pure as yours, then I shudder to even think of the consequences.”
Hard to be a God, chapter 9.
Thus, seeing that Rumata could not be swayed by the means of persuasion, Arata decided to try a more blunt method: make it sting for Rumata, by killing the one person he truly cared for on this planet. Rumata would then use the lightnings himself, and cause at least some destruction to the lords and oppressors Arata hates so much.
Arata could also have seen Rumata as having betrayed him, by saving him, providing him with money, but not giving him weapons.
“Once I had a friend,” he said. “You’ve probably heard of him - Waga the Wheel. We had begun together. Then he became a bandit, the king of the night. I didn’t forgive him for his treason, and he knew it. He had helped me a lot—out of fear and self-interest—but he never did want to come back. He had his own goals. Two years ago his people gave me up to Don Reba.” He looked at his fingers and curled them into a fist. “And today I found him in the Port of Arkanar. In our business, there’s no such thing as half a friend. Half a friend - that’s always half an enemy.”
Hard to be a God, chapter 9. Emphasis mine.
The essay you speak of gives a different interpretation. It claims that Arata was a ruthless manipulator, and it would be him, and not Don Reba, who would benefit from killing Kira: chaos caused by Rumata's raging would help Arata stage another uprising. We do not know if this actually happened, since our knowledge of the events in Arkanar is limited to the moment the patrol airship dropped sleeping gas on the city.
It is, however, interesting that this scene did not exist in the brothers' original manuscripts. It was added after (friendly) requests by editors:
Everything in this novel was unusual to [editors], and a lot of requests (quite friendly, by the way, and not at all meanly critical) were made. On the advice of I. A. Efremov, we renamed the Minister of the Defense of the Crown Don Reba (he had previously been Don Rebia - an overly simple anagram, in the opinion of Ivan Antonovich.) Moreover, we had to do a lot of work on the text and add an entire big scene where Arata the Hunchback demands lightning from the hero and doesn’t receive it.
Afterword by Boris Strugatsky.
I'm not at all sure as to why the editors would want this scene added - possibly they were trying to do exactly this - shift the blame from Reba to Arata.
It is easy to notice that the chapter is very short, and if one was to read the book with this whole chapter missing, nothing would be lost from the plot, and there would be absolutely no reason to suspect Arata as having planned anything against Rumata.
Author's stance that it was Reba who ordered the abduction, is much stronger.
It is far more likely that Reba was intended as the wannabe abductor or killer. Notice the following lines:
“We’re all operatives,” said Don Condor. “And all that is precious to
us must be either far away on Earth or inside us. So that no one can
take it away and use it as a hostage.”
“You’re talking about Kira?” Rumata asked.
“Yes, my boy. If all I know about Don Reba is true, keeping him under control is a difficult and dangerous task. You see what I’m trying to say.”
“Yes, I see,” Rumata said. “I’ll try to think of something.”
Hard to be a God, chapter 10.
As one notices from reading further, Rumata could've thought of something faster. It is at least strongly implied in the text that Reba was behind this, and if the author acknowledges this, it is probably true.
Don Condor has all but prophesised the outcome, being more experienced and knowledgeable in feudal affairs.
It's also not clear whether Arata could have known Rumata would be going to the Drunken Lair: Arata leaves immediately after their conversation, and I would assume he headed to get the money, and then start some more rebellions.
Reba openly attached a spy to Rumata, so he would be notified when Rumata and his friend left on horses (implying a long ride); Arata, on the other hand, seems more like a lone wolf type - it is unlikely he had a network of spies, and while he could have had the money, it is unlikely he would have ordered mercenaries to abduct Kira, let alone the fact it weren't even mercenaries that came - it were monks, who obey Don Reba.
“In the name of the Lord!” roared below. [...] There were numerous riders outside - sullen men in black with pointed hoods.
Hard to be a God, chapter 9. Emphasis mine.
Arata did not have power over them - they'd immediately quarter him for all the "good" he's done.
Also, Arata regarded Rumata as a god:
“Don Rumata, do you remember how disappointed I was when I found out who you are? I hate priests, and it was very bitter to me that their false fairy tales turned out to be true. But a poor rebel must draw benefit from whatever circumstances he encounters. The priests say that the gods have lightning. Don Rumata, I really need lightning to break down the fortified walls.”
Rumata gave a deep sigh. After the miraculous helicopter rescue, Arata had insisted on an explanation. Rumata tried to explain about himself; he even pointed out Earth’s sun in the night sky—a tiny, barely visible star. But the rebel only understood one thing: the damned priests were right and there were gods living behind the firmament who were all-good and all-powerful. And since then, he steered each of his conversations with Rumata to one thing: God, since you exist, give me your power, for it is the best thing that you can do.
Hard to be a God, chapter 9. Emphasis mine.
It would be unlikely for Arata, who is an extremely cautious person (having survived thus far, at least) would want to angry a person he regarded as a god, especially given he knew that Rumata had a helicopter ("iron bird"), which would mean he'd be able to traverse the distance between the Drunken Lair and his house on short notice, which conflicts with the objective given to the monks:
“They always mess things up,” someone said softly downstairs. “The master’s at home.”
“What’s that matter to us?”
“It matters because he’s the best swordsman in the world.”
“And they also said that he left and won’t come back till morning.”
Hard to be a God, chapter 9.
All and all, all of this has a very distinct stench of Reba, and not a musk of Arata in it.
