Electrically, really no effect besides you have one-half as much voltage drop on the neutral.
Feeder neutrals are sometimes sized larger than ungrounded conductors (either through a larger wire size or parallel conductors) to carry high harmonic currents that may be present due to nonlinear loads (a common way this is specified is a "200% neutral"). In this case, it is possible that at times you may only have one load in use that is connected phase to neutral, essentially creating the same situation you describe, just on a feeder instead of a branch circuit.
It is really a waste of wire more than anything else, there is not really any practical difference. Especially since if you have equipment that requires a 2 pole breaker and a neutral, the majority of the current is often drawn phase to phase, and the neutral current is typically significantly lower. Although it is impossible to tell without knowing the specific equipment.
Code-wise you have an issue with 310.10(H)(1) if the paralleled conductors are smaller than 1/0.
You would also count both neutrals when counting current carrying conductors, which results in more than three current carrying conductors (since there are 4), so the adjustment factors of 310.15(B)(3)(a) would apply. Unless the neutrals are only carrying the unbalanced load of the ungrounded conductors (such as in 120/240 split phase), then they do not need to be counted (310.15(B)(5)(a)).
