FYI I wondered if B::Deparse could show this. The answer is yes, with level 5 of deparsing or higher, use statments will be translated into their equivalent BEGIN blocks:

perl -MO=Deparse,-x5 -e "use Set my $x = 12;"
sub BEGIN {
    require Set;
    do {
        'Set'->import(my $x = 12)
    };
}
-e syntax OK
[download]

I don't think the fact that the lexical has a scope even shorter than the BEGIN block changes anything though.