Am I allowed to use archaic words in Quiddler/Scrabble?
The word legality rules of Quiddler appear to be slightly more relaxed than those of Scrabble - according to Wikipedia, capitalized adjectives such as "Iraqi" and "Scottish" are acceptable in Quiddler, where to the best of my knowledge they still aren't in Scrabble.

Archaic words, by contrast, have always been allowed in Scrabble.  Again per Wikipedia: 


  "Variant spellings, slang or offensive terms, archaic or obsolete
  terms, and specialized jargon words are allowed if they meet all other
  criteria for acceptability."


So I'd say they were definitely fair game for Quiddler too.  Having said all that, both Scrabble and Quiddler are games that lend themselves well to house rules.  If you're playing with your grandmother you're probably going to dial back on the offensive terms; likewise some people get so offended by the idea of allowing slang or archaisms that it can become easier just not to use them!

As a side note, the funny thing about "quo" is that I suspect most people try to use it as part of the phrase "status quo" - which would be a foreign phrase and therefore not acceptable!  But luckily your dictionary contains a legitimate form of it also.