It should do easily, the 2.35 is more like a 2.1, the 2.5 isn't that big, certainly no bigger than a lot of other 2.4's.
The high roller 2 is more accurately sized.
I'd recommend specialized eskars, I've used (and really rate) various high rollers, but the eskars feel like a better compromise. More grip than a 2.35 60a singleply, nowhere near as draggy as a 2.5 supertacky, and only slightly heavier than a singleply 2.35.
Saying that what are you doing in the alps, if it's all chairlifts just get a pair of 2.5 super tacky dual ply's, instantly transforms any bike into a DH bike, so much weight, but stupidly grippy and you'd have to try hard to puncture one.
XC - 2.35 singleply 60a/maxxpro
AM - eskars (might even get away with something faster on the rear)
DH - 2.5 dual ply 42a/supertacky