Will valves hit pistons if too much is resurfaced off of head?

Will valves hit pistons if too much is resurfaced off of head?
It's definitely possible in theory, but really depends on the specific parts involved, what their clearances were to begin with, and what the timing is. I suspect that by the time you mill that much off of a head, you may wish to consider that it may be unuseable for other reasons like maybe compromised strength or something.

Also worthy of note, in some applications, doubling up the head gasket is possible. People who do so usually do it to increase the engine dispacement by a small amount for whatever reason, but it could also serve to regain lost clearance due to overmilling.