OK, I'm just a student pilot, and not a taildragger student either.
But I know a little physics. The CG is still behind the mains even
with the tail up. It is possible that the airplane would feel more
stable in yaw when it is accelerating, however. Since the center of
gravity is being pulled along behind the propeller, I would think the
airplane would tend to stay in line. This ignores other influences
like crosswinds and the torque effects of the prop which would tend to
counter this. And it won't help you in taxiing when you are moving at
a constant speed.

Yes, you are right about the CG not changing, I was probably
mistakenly thinking that the CG moves forward relative to the ground
as the airplane nose is "lowered" but I think that's not correct. The
stability in a level attitude while taxing probably also comes from
the fact that the P-factor is gone and there is no turning tendency
any more.