It's called "decking", and 1/16" would be far too much to remove. That's .0625", and the usual amount of block machining is about .015" or so, just enough to level out the gasket sealing area, and correct any warp. If the head gasket sealing area is badly pitted, there's another way to correct the problem. Is the block being bored as part of the rebuild? If so, have the machine shop install some short sealing rings made from a cylinder sleeve slightly larger than the bore size, stopping just above the travel of the top piston ring. I've saved blocks that had grooves eroded in them from running with a blown head gasket for a long time this way. If the repair ring is installed before the rebore job, it will be almost invisible, and very effective after the block is rebored for the new pistons. I've cut repair rings from a 1/8" wall cylinder sleeve and installed them in several damaged blocks, then run them in race engines, without any failures. "Flanged" cylinder sleeves are also available for such repairs, but they're pricey, and installing all 6 of them would be more expensive than finding another block to work with!
Jerry