How long will cheap oil transfer pump survive pumping water?

So your plan is to switch the pump on and off as the catch bucket fills to a certain level, and not have the pump run constantly?
Water acts as a lubricant, though obviously much less effective than oil. The pump could very well live two hours not running constantly. I haven't seen it in years, but some water pump lube in the water could help the pump live long enough.
As Inertia said, I'd worry about it losing prime and not being able to re-prime. This might be able to be managed by carefully watching the level in the bucket, and not allowing the pickup to get uncovered. Or having some way to gravity feed the pump.
If I were you, I would buy two pumps, and test your solution with one knowing you will probably damage it severely. If it works well enough, use the second pump in the parade. If the plan doesn't work, return the unused pump at your convenience. All time permitting, of course.
Good luck!