Anecdotal: as a shared hoster engineer I would say yes. Ten years ago there were loads of Perl apps running on our shared Linux and Windows boxes, these days it's a novelty to bump into anything written in Perl.

server-side as in... shell scripts/daemons?

or server-side as in... cgi/fastcgi serving to a client?

because I would say 'yes' to cgi/fastcgi, but 'no' to shell scripts/daemons.

There are a handful of really cool newish Perl frameworks, but unfortunately I think Perl 5's stigma is so far out there it will never gain any real traction. It seems that Perl 6 has a lot of the same stigma attached to it. I almost wish they would name it something other than Perl so that a fresh perspective could be used, it seems like it's going to be quite nice!