Yeah, Godsized are awesome. Knew nothing about them and saw them opening for Black Label Society. They rocked so hard and had amazing tone. BLS could not keep up at all.
Yes if I recall correctly the Abraxas is somewhat of a hotter overwound version of the Mule.
The wood does affect the sound a lot. Everything has an effect, somethings more, somethings less, but the wood is a pretty essential part. A lot of things can be concidered as they affect tone: strings (material, construction method, thickness of core wire and wind, etc), pickup height, woods (quality, combination), contruction method of the guitar, hardware, etc....
Some PUs sit very well in certain woods, less in others. Like the HD is said to exell in basswood and in all mahagony the Riff Raff is very nice.
It is about complementing qualitys and iron out shortcommings of the wood.
Donīt know enough about the BD or basswood to though to make a proper judgement about that combo though, gotta leave this other guys.