Nabokov sometimes used translations into English as an opportunity to touch up his work, but sometimes he didn't. Below are a few case studies.
Maybe the best example of Nabokov making changes is Laughter in the Dark, the author's rewrite of Winifred Roy's 1935 translation of the Russian Kamera Obskura.
Colapinto has a piece in the New Yorker called How Nabokov Retranslated "Laughter in the Dark" (2014) which describes the changes Nabokov made to Roy's translation. It turns out that Nabokov worked directly from Roy's translation in composing Laughter.
Here are just some of the changes that Nabokov made:
He changed all the character names.
He added the early film scene which foreshadows the book's end.
He changed the age of the heroine from Roy's "seventeen or eighteen" to sixteen.
He substantially re-worked the opening to increase its speed. (This includes adding the memorable passage about the animated Bruegel painting and changing the mechanism by which Axel Rex is introduced).
He made minor changes to imagery (such as adding the imagery of the "frozen wave" of carpet to the final scene).
He changed the mechanism by which Albinus discovers Margot's infidelity (which involves replacing the character of Segelkranz with Udo Conrad).
It's clear from Laughter that at least sometimes Nabokov used translations as an occasion to substantially touch up his work.
That said, in the 1970 foreword to his translation of Mary (with Michael Glenny), Nabokov explicitly declares that he did not make any substantial changes to the work. He writes:
I realized as soon as my collaboration with Mr. Glenny started that our translation should be as faithful to the text as I would have insisted on its being had that text not been mine. Revampments of the lighthearted and highhanded order that I used for the English version of, say, King, Queen, Knave could not be envisaged here.
The only adjustments I deemed necessary are limited to brief utilitarian phrases in three or four passages alluding to routine Russian matters (obvious to fellow-émigrés but incomprehensible to foreign readers) and to the switch of seasonal dates in Ganin’s Julian Calendar to those of the Gregorian style in general use (e.g., his end of July is our second week of August, etc.).
Nabokov may have left Mary alone, but he does admit in the above passage that he made "revampments of the lighthearted and highhanded order" to King, Queen, Knave. In fact, he admits as much also in the foreword to that book, where he writes:
By the end of 1966, my son had prepared a literal translation of the book in English, and this I placed on my lectern beside a copy of the Russian edition. I foresaw having to make a number of revisions affecting the actual text of a forty-year-old novel which I had not reread ever since its proofs had been corrected by an author twice younger than the reviser. Very soon I asserted that the original sagged considerably more than I had expected. I do not wish to spoil the pleasure of future collators by discussing the little changes I made. Let me only remark that my main purpose in making them was not to beautify a corpse but rather to permit a still breathing body to enjoy certain innate capacities which inexperience and eagerness, the haste of thought and the sloth of word had denied it formerly. Within the texture of the creature, those possibilities were practically crying to be developed or teased out. I accomplished the operation not without relish. The “coarseness” and “lewdness” of the book that alarmed my kindest critics in émigré periodicals have of course been preserved, but I confess to have mercilessly struck out and rewritten many lame odds and ends, such as for instance a crucial transition in the last chapter where in order to get rid temporarily of Franz, who was not supposed to butt in while certain important scenes in the Gravitz resort engaged the attention of the author, the latter used the despicable expedient of having Dreyer send Franz away to Berlin with a scallop-shaped cigarette case that had to be returned to a businessman who had mislaid it with the author’s connivance (a similar object also figures, I see, in my Speak, Memory, 1966, and quite properly, too, for its shape is that of the famous In Search of Lost Time cake). I cannot say I feel I have been losing time over a dated novel. Its revised text may soften and entertain even such readers as are opposed, for religious reasons no doubt, to an author’s thriftily and imperturbably resurrecting all his old works one after the other while working on a new novel that has now obsessed him for five years. But I do think that even a godless author owes too much to his juvenilia not to take advantage of a situation hardly ever twinned in the history of Russian literature and save from administrative oblivion the books banned with a shudder in his sad and remote country.
Lastly, I should like to mention an apt quote from the foreword to Invitation to a Beheading, where Nabokov explicitly describes his urge to emend his previous work. He writes:
If some day I make a dictionary of definitions wanting single words to head them, a cherished entry will be “To abridge, expand, or otherwise alter or cause to be altered, for the sake of belated improvement, one’s own writings in translation.” Generally speaking the urge to do this grows in proportion to the length of time separating the model from the mimic; but when my son gave me to check the translation of this book and when I, after many years, had to reread the Russian original, I found with relief that there was no devil of creative emendation for me to fight. My Russian idiom, in 1935, had embodied a certain vision in the precise terms that fitted it, and the only corrections which its transformation into English could profit by were routine ones, for the sake of that clarity which in English seems to require less elaborate electric fixtures than in Russian. My son proved to be a marvelously congenial translator, and it was settled between us that fidelity to one’s author comes first, no matter how bizarre the result.
In this passage Nabokov confesses his desire to emend his earlier writing, while also observing that he found no need to change Invitation.
In conclusion, sometimes Nabokov used translation as an occasion to make drastic changes (as in Laughter in the Dark and King, Queen, Knave), but sometimes he didn't (as in Mary and Invitation to a Beheading).