You would probably not do any damage if you dont turn the front wheels. PT4WD can function on the pavement for straight line travel, but I wouldn't do it often.
In PT4WD the front and rear driveshafts are locked together. This will cause driveline binding if you turn the vehicle because the front and rear wheels will not be turning the same speed. If traveling straight, there is little potential for binding, however if you have tires that have slightly different diameters (different inflation levels, different loading, etc), you could have some minor binding.
I dont think you would get any benefit in a race by using PT4WD versus FT4WD. You may see a slight benefit if comparing PT4WD with 2WD since PT4WD would prevent the tires from breaking loose in a hard accel.