Damage hole in seat tube after sandblasting, is it possible?
The picture lacks the resolution needed. Rust can creep under paint from a small chip, and in that spot(behind the seat tube you say?) it would get a large amount of water and slop. As for the shop, a bad operator with the wrong blasting abrasive can easily erode a hole like this, with a reasonable operator it is not likely, even a brass plug should be safe unless it was soldered improperly and basically fell out.

Do not leave it open or it will collect splashes, condensation, and then rust inside. A spot of siloxane/silicone caulk or gasket maker will suffice, get clear or try to match the color a bit. Another option is a smooth/round headed sheet metal screw of the right diameter, "thread cutting" type.(fine thread not the coarse "self tapping" sort)
 Be sure to dope the threads with some low strength loc-tight, grease, or gasket maker(only one, not all three) so it doesn't rust in place or rattle out.