Yes, LWP::Protocol::https is installed. I can compare exact version numbers with the user, but we both installed modules from PPM (Perl Package Manager) not from CPAN.
Comment on Re^2: WWW::Mechanize cannot connect to HTTPS site
You'll probably experience problems with out of date dependencies, things like Mozilla::CA need to be reasonably up to date. IIRC ActiveState cut off PPM access for older perls without a support contact in place.