Broadly, the answer is yes. Allen Ginsberg summed this up well when he laid out his characteristics of beat literature in 1982, two decades after the beat movement had burned out and thus plenty of time for him (and others) to retroactively decide what defined the movement. His first - and it's noteworthy that it was his first - characteristic was:
Spiritual liberation, sexual "revolution" or "liberation," i.e., gay liberation, somewhat catalyzing women's liberation, black liberation, Gray Panther activism.
However, this definition also encompasses the problem with this aspect of beat literature: to them, with their intense focus on individuality, "spirituality" was very much a personal choice. It was up to the individual to decide what it meant to them and, by extension, what spiritual fulfilment entailed. You can see this in the wildly different approaches to spirituality that the key beat authors took themselves.
Take Kerouac, for instance. He was raised, and remained, a devout Catholic all of his life. However, unlike most Catholics, he became interested in and experimented with Buddhism, indicating a far more flexible attitude to spirituality and redemption than, say, his very devout Catholic mother. One of his novels, The Dharma Bums, has the direct connection to spirituality the title suggests.
He wrote his more famous work, On The Road, with a list of dictums above his desk which included:
Be crazy dumb saint of the mind.
And of the book itself, he said it was:
a story about two Catholic buddies roaming the country in search of God. And we found him. I found him in the sky, in Market Street San Francisco (those 2 visions), and Dean (Neal) had God sweating out of his forehead all the way.
And when you read On The Road you can see very frequent references to religion and religious symbolism. Here are a few I picked out at random:
I would be strange and ragged and like the prophet who has walked across the land to bring the dark word and the only word I had was “wow.”
"Everything is fine, Sal," he said. "God exists!"
‘There he is! That’s him! Old God! Old God Shearing! Yes! Yes! Yes!’
The strange thing was that next door to Remi lived a Negro called Mr. Snow whose laugh I swear on the Bible was positively and finally the one greatest laugh in all this world
Indeed it's quite possible to see Dean in the book as a Christ-like or prophet-like figure and Sal as his follower or disciple. Although it's worth noting that with his promiscuity and irresponsibility, Dean is a long way from the actual Christ, illustrating again the width of what passes as spirituality for the beats.
Religious symbolism is everywhere in Ginsberg's Howl, and it's certainly not confined to his Buddhist beliefs or his Jewish background either. Indeed in his evoking of a wide range of religious and magical symbols, you can see reinforced his liberal belief in people needing to find spirituality in their own way rather than following a dogmatic belief system. Again, here are a few examples:
who bared their brains to Heaven under the El and saw Mohammedan angels staggering on tenement roofs illuminated
who fell on their knees in hopeless cathedrals praying for each other’s salvation and light and breasts, until the soul illuminated its hair for a second
where you accuse your doctors of insanity and plot the Hebrew socialist revolution against the fascist national Golgotha
And then there's the whole of section two where "Moloch" - a Canaanite deity mentioned in the bible - stands in for the military-industrial complex, plus the footnote with its repeated evocation of "Holy". This fondness for religiosity isn't just confined to Howl either: witness the title of his collected early works, The Book of Martyrdom and Artifice.
Burroughs is a more complex case, but then Burroughs is a strange figure within the beat movement - older than the rest of its characters and ruggedly libertarian. However, he flirted with religious movements all his life. Most notably this took the form of a lifelong belief in "magic" which went so far as to see him actively practising concepts such as scrying and cursing his enemies. He was also interested in Buddhism and was, briefly a member of the church of Scientology.
I'm much less familiar with Burroughs' work than that of Kerouac and Ginsberg but he was also fond of religious iconography in his work:
Dusk was falling and blue shadows gathered in the Sangre de Cristo Mountains to the east. Sangre de Cristo! Rivers of blood! Mountains of blood! Does Christ never get tired of bleeding?
“Buddha? A notorious metabolic junky . . . Makes his own you dig. In India, where they got no sense of time, The Man is often a month late . . . Now let me see, is that the second or the third monsoon? I got like a meet in Ketchupore about more or less.’
And Burroughs himself is on record as stating his belief that writing itself was magical and had a magical purpose, helping the reader to move beyond everyday consciousness.
While there doesn't seem to be much evidence of religion among the lesser beat figures - Neal Cassidy, whom we've already discussed, aside - Kerouac, Ginsberg and Burroughs are the core writers of the movement and those who've found lasting fame within it. And they were certainly "spiritual" althought not really in a sense that any organised religion would accept. The beats have been criticised as anti-intellectual and their approach to religion is open to the same charge of wooly thinking. But then again, that lack of cohesion is part and parcel of what the beats wanted to achieve, so perhaps taking them to task for it is missing the point.