i chase holes all the time with the carbide endmillthings (the ball end ones) that dremmel has in 1/8 and 3/32 size in alot of ways i wish they made a 3/16 size too
the fact that they have liek 10 flutes helps with not having out of round holes
i undersize drill HT then chase the hard steel no problem
the vice set up is also the best plan as i have one on my mini mill