Of course you can, and this technique is used by many. In fact, with the chamber bored true to start, the pilot on the reamer is superfluous. When rechambering a barrel in which the existing chamber is eccentric, you can bore the existing chamber and end up with a decent job. It will still be necessary to set back in order to correct an eccentric throat and neck. The barrel is indicated at the location of the new throat, then bored to true up the body of the chamber. It can be bored to match the body taper of the new cartridge, or it can be bored straight at about .010" under the shoulder diameter. Either way will give a straight start. I have used this method many times. GD