Sort of. When I hear Nabokov speaking, he sounds like he has an unplaceable regional accent, as opposed to a "foreign" one. His writing in English is fluent, but can have a few tics in it — he repeats certain fancy words, and he tends to avoid slang.

By the way, the last tsar's daughters reportedly picked up a slight Irish accent from one of their tutors. He was sacked and replaced by someone more pukka.