Yes, you can run the engine while the drive shaft is removed, with or without water (make as necessary, plumbing connections if using cooling water). Of course no water is necessary if running time is kept short (~30 seconds). The only danger of running without pump and drive shaft is, if the PTO wheel unscrews from the threaded crankshaft (a possible rotating hazard can occur) but this shouldn't be a problem for a used engine b/c the PTO will already be tightly threaded onto the crankshaft by historical torque, still, beware of the potential rotating hazard.
Whether or not to rebuild the carbs first depends on how well the engine starts, if the carbs are working well already the engine should start easily (I think you can test this before installing the drive shaft). Of course if the engine has not been started in 5 months, it will naturally be more difficult to start at first b/c the normally residual fuel will have evaporated from within the crankcase over the period.
For instance, I started my engine last weekend for the first time since October and it required a bit of extra cranking(with choke applied) b/c the fuel had evaporated from the carbs and crankcase, I also had drained the fuel tank and the fuel lines were most likely dry as well.
Seems like many new wear rings are tight around the circumference of the impeller, causing difficulty starting the engine. So if the engine is hard to start already (b/c it hasn't been started in 5 months) even without the extra friction, then it may be impossible to start once the tight pump is reinstalled.