Rusted Laboratory Key [???]

So you may know ??? has 3 stages; Meteor Puzzles; Lab N; Old Meteor/Mehme's Wooden House.
Can you skip the whole Lab N part if you already have the key? You get the 3 shards from meteors, and then, you already have the key... So you can skip Lab N? But only you can do it in that case, because your friends don't have it... Or can you cheat it?
Hmmm...
Does it actually get a [Quest Book Updated] when you complete a puzzle?
(I'm asking this because I want to get cosmic for my archer, so I can grind faster, I have already done the quest with my assassin.)

 

I don't think that it does but you'll still have to do it I think, for the necklace of 1k storms it's a discovery but you need to go through steps to get it.