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Yes, a drill press can drill a square hole. Mortice and tenons have been used in woodwork for centuries, a mortice chisel is a part of this process.
A drill press and mortice chisel and jig drills square holes for mortice and tenon joints easily and quickly. The auger in the mortice chisels is positioned just below the tips of the chisel, and drills a hole with the square corners of the chisel then removed the rest of the timber creating a square hole.
This chisel will drill from 3/8" in one pass, and has a 3/4" chisel shank