I think that's a bit too clever. What if there is a global variable named $regex? You've just clobbered it. I think creating a local alias is probably better.

use strict;
use warnings;
sub regex {
    my $in = shift;
    my $ret = '';

    # Assign something to $ret in a code assertion
    local *alias = \$ret; 
    $in =~ m/^(a)(?{ $alias = 1})/;

    return $ret;
}

while(<DATA>) {
    print regex($_) . ".";
}
print "\n";

__DATA__
a
b
a
abcd
bcda
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-sauoq
"My two cents aren't worth a dime.";