With some bikes it is. You should find somebody with a 27.5 wheel (with tire on it) and see if your bike was built with enough clearance for it to be possible.

 

It looks like it has enough room but that's prob a good starting point haha

 

A 2.7 tire will probably not fit under the fork arch, unless someone traded out the standard single crown fork for a dual crown "DH" fork.
There's a thread cataloging most of the 27.5 capable bikes somewhere here, and the general consensus is IIRC, that a 2.3ish is the biggest volume you can make work on a standard fork.
Obviously the rear is more subjective, but probably not dramatically different.

 

Why? Just to be trendy?

 

They probably won't fit. The chainstay bridge doesn't have a huge amount of clearance like the seat stays do.

Just a suggestion:You probably won't get much benefit from the larger wheels, if that's what you're hoping for. One of the selling points of larger wheels is their ability to maintain rolling velocity a bit better. The difference between 26 and 27.5 is pretty darn small (a few percent, give or take). The Stinky has quite an inefficient suspension design for pedaling, so the few percent better rolling efficiency would likely be all but cancelled out completely by that. What I mean to say is that you probably won't notice any appreciable difference with 27.5 wheels. I say don't bother wasting a bunch of money to keep up with current trends and gain nothing from it. Ride what you have and enjoy the heck out if it.