Unless it's started with debugging enabled, no I don't think there's a way to get an existing process into the debugger. However having said that you probably could come up with a creative combination of PERLDB_OPTS and a subroutine which you trigger somehow (say sending your process a SIGUSR1) that sets $DB::signal to make it so that you can get it to drop into the debugger on demand rather than from the start. See perldebtut, perldebug, and perldebguts for more hints (and I don't want to hear any complaints about performance if you run everything under the debugger :).
(And as a parenthetical aside, it'd be cool if there was some way to do something in Perl akin to the Ruby on Rails breakpoint / script/breakpointer setup. That lets you have breakpoint calls in your Rails code and then you run the breakpointer script which attaches to an irb (interactive Ruby; think perl -de 0) session which interacts with the Rails app via DRb calls.)