Yep, you are right. From perlre
WARNING: Once Perl sees that you need one of $&, $`, or $' anywhere in the program, it has to provide them for every pattern match. This may substantially slow your program. Perl uses the same mechanism to produce $1, $2, etc, so you also pay a price for each pattern that contains capturing parentheses. (To avoid this cost while retaining the grouping behaviour, use the extended regular expression (?: ... ) instead.) But if you never use $&, $` or $', then patterns without capturing parentheses will not be penalized. So avoid $&, $', and $` if you can, but if you can't (and some algorithms really appreciate them), once you've used them once, use them at will, because you've already paid the price. As of 5.005, $& is not so costly as the other two.
s aamecha.s a..a\u$&owag.print