If they run out of air, they will abandon their post by your side and swim to the surface.

However, they do not have infinite breath (with the exception of Derkeethus, the only Argonian follower) unless you give them a waterbreathing enchantment to wear (see Follower Equipment below). Followers do not take Water Damage, and cannot drown. Skyrim but it's destroyed by mods - Duration. Skyrim Hidden Argonian follower 217 Adaptive Perspective.