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Things that glow under UV light are taking in UV, and giving off visible light. The brighness of the glow is directly related to the strength of the UV light, but for the kind of event you are talking about, the glow could be pretty dim. Obviously the ambient light level will make a bid difference as to how things will show up, but I would guess you should be prepared for some very low light levels of both the ambient and the UV glow. Do you happen to have one of the newer cameras that do pretty well in low light? For one project I shot, where the light level was pretty low and changed quite a bit, I shot with a fast lens wide open on manual with a fixed shutter speed that I could hand hold, and then used Auto ISO with no limit on how high the ISO would go. I had a lot of keepers doing that. It is of course difficult to auto focus in low light, so be prepared to do manual focus by eye, or even focus by setting the distance scale on the lens.
You should for sure try things out with the AV company, even if it is just a quick test in a small room. You should probably be prepared with a flash that you can bounce off the ceiling and set the power very low, so that you can suplement the available light a bit, but only at a low fill level that does not overpower the UV glow on the guests. And remember, because of the unusual situation, you have a built in excuse to have limited depth of field, motion effects, poor color balance, and lots of noise showing in the images. Shooting from a tripod and having lots of planned motion effects is another approach that could come out well.