It seems likely to me that the shape of the vibration of the top of the guitar will be changed. A flat-top (pegbridge) guitar top is twisted by the string tension when played, so the vibrations will not be symmetrical (even if the top of the guitar were round and there wwere no soundhole).

With a Bridge Doctor, the twist is removed and the top acts more like a piston.

I expect this to reduce the harmonics. I expect this to make the guitar sound more like a tailpiece guitar rather than a pegbridge.