`grep' in Perl is a misnomer; it's not inherently related to RExen. It should really be named `filter' or something similar. As such, using a bare variable as the `EXPR' in grep EXPR, LIST won't invoke the REx engine at all -- basically you're checking $searchtext for truth each time through the `LIST', which is most certainly not WYM.
My personal vote on this problem would be to provide the users a radio button group allowing them to choose whether they want to use Perl-based or standard search-engine searches, rather than trying to come up with a heuristic to determine if $searchtext is a Perl REx or just a term.
However, if you really want to do that, you'll want to look into `\Q' and `\E' to quote characters in a REx, rather than going to all that trouble (on line 4) to take care of metacharacters. I'm skeptical of the conversion from `*' to `\w*', but I suppose it's a sensible choice.
Rather than trying to build up a string that syntactically resembles a REx in Perl code, build the actual search pattern and then use it in the grep inside of a REx:
grep m/$searchtext/, <STUFF>
You might also want to look into qr// for a more efficient and cleaner way to build RExen programatically.