That would work, can do 7 glasses a min. That means means 420 glasses an hour, which would be 840 glasses in the two hours. The question was about hundreds of guests and not thousands so your operating at the top range of that.
Large commercial hotel. It's not impossible they don't have this sort of equipment already.
The problem with checks like this is that you need to be intimately aware of the capabilities of an organisation to know whether it's reasonable or not. As people who work with technology know, things that seem impossible to the uninitiated can be remarkably trivial. We should probably assume that others have similarly impressive capabilities in areas we don't understand.
The advantage of the Van Halen test over this is that it's simple for everyone. This seems needlessly "clever" and is as a result wrong...
Definitely possible!