Sounds like it does. It's just unlikely to happen in most solutions where the number of water molecules far outweighs the number of hydronium ions.
I'll also add that under almost all conditions, the formation of H2O2+ is probably very thermodynamically unfavorable compared to hydronium formation. This means that even if the concentrations were equal, the formation would still be less likely to occur due to instability of the molecules.
Think about it: why would a charge accumulate on one molecule when it could spread itself out?