Can I use this with a tapered drill bit with the counter sink attached?

This is not designed to be used with a countersink. As you have stated, you can drill the hole without the countersink first, then go back with the countersink.

I think I just figured out the answer to my own question. From where I have the countersink set on the bit to make a hole without the drill block, I need to remove the counter sink and go up the height of the drill block about an inch and a quarter and then drill the hole without the counter sink and then come back at the end and make the counter sink hole. A little more work but my whole should be straighter than without the assistance from the drill block.