Yes, but it is perfectly reasonable to expect that Perl might recognize  /$foo/ or  /$foo/g as being able to re-use a compiled expression instead of compiling a new one. This is what I think the OP was asking, and I am confirming that no, Perl does not recognize these special cases. The only way to take an unknown regex and efficiently plug it into code that does anything more elaborate than  ... =~ $foo (and gets called more than once, because it will only matter if the code gets called in a loop or something) is to eval an entire sub with the regex expanded within it.
It might help to know that m// and m//g are realized as separate commands in other languages.

Yes and in those languages, you can usually create an object to represent the compiled regex and then get either/both operations out of one compilation. Unfortunately perl can't do this easily.

Edit: Perl does special-case these, actually. Just not anything more elaborate like prefixing  /\G$foo/ to change the anchor.

In reply to Re^3: On the regex pattern variable to be inserted into another by NERDVANA
in thread On the regex pattern variable to be inserted into another by Anonymous Monk

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