My understanding, from reading aforesaid document, is that my $var if $test; is undefined.

But the cited doc in Re: postfix syntax enlightenment sez "NOTE: The behaviour of ... is undefined.", clearly, I think, referring to behavior (or behaviour, if you will) rather than to the state of the lexical being undef (if I correctly understand your understanding). (The link is to 5.18.2 docs, but my local 5.10.1 docs say essentially the same, but without reference to state or our.)