Will my beard grow back after radiation therapy?

Possibly not. There can be some thining of the hair in the treatment field of radiation. Thining of facial hair after head and neck radiation is a possibility same with hair loss of the scalp after whole brain radiation.
Probably. It depends on the dose delivered to the skin. In head and neck cancer the facial hair falls out where the radiation beams go through. If older methods are used many times it comes back but very sparse. In newer imrt methods then radiation is spread out more and even though it still falls out the skin dose may be lower and the hair has a chance to recover.