Can you dry-fire an Airgun?

NO, Dry-Firing an airgun is not recommended, especially if you have a Spring Piston variety!

If you don’t have a pellet in the breech then there won’t be a cushion of air protecting the piston from slamming hard into the internals of your gun. This does your seals no good at all and will shorten the life-span of your gun.

There is at least one manufacturer (Gamo) who creates most of their rifles in such a way that it doesn’t matter as much if you accidentally do this, but they still don’t recommend it.