I have to agree with those advising extreme caution. Long time machinist here (in my past occupation) and I'd likely not. At the absolute least buy your bits from a legit industrial supply like
here. That drill press would work as long as it has a quality chuck like a Jacobs that runs true. You'll need a good ratcheting tap handle too. And possibly a bushing guide to start it and keep it straight while cutting the threads if your workpiece allows its use.
Also you will save yourself a lot of heartache if you use the actual drill size for the tap. Standard sets very rarely have the proper size to work. Consult a tap/drill chart. And I'll double down on the TIN coated drills are not all equal. I got one from a big box store that was pure garbage. Wouldn't even drill mild steel and the drill was probably mild steel itself. Again...buy from a machine tool supply company.