Yes, that's likely the culprit.
WWW::Mechanize is a wrapper for LWP::UserAgent. As of version 6 of LWP (released quite recently), HTTPS support (in LWP::Protocol::https) was spun out into a separate distribution, so needs to be installed separately.
In reply to Re^6: Mechanize not working with HTTPS
by tobyink
in thread Mechanize not working with HTTPS
by omegaweaponZ
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