Will new bottom plates in basement allow radon penetration?
If you have radon, it's already likely getting in--concrete is permeable. So adding a small nail hole isn't going to change anything. Also note that tapcons don't actually penetrate all the way through the slab.

If you have radon, you need to get a radon remediation system installed. This will put a hole in your slab so the radon has a place to go (and then it's vented out the roof).