Yes, the archery skill tree is affected by and effects both bows and crossbows. Any perks you get on the archery tree will also work on crossbows.

Do crossbows benefit from archery perks Skyrim?

Everything that affects bows affect crossbows as well (damage multiplier etc), even Deadly Aim . Those perks that aren't immediately obvious work like this: Hunter's Discipline - more bolts (from mobs who drop bolts in the first place) Ranger - move faster while aiming and reloading.

Does archery count for crossbows Skyrim?

Yes they do. When I got my first crossbow, I tried it out. I hadn't used bows at all and leveled up after a few shots.