Will the marble slurry I collect in a wet vac be safe to dispose of down the drain?

This will depend on what type of sewage system the drain has. If you are dumping slurry down the drain and the systems is on a septic tank you take the chance of upsetting the delicate balance of the septic system and killing the bacteria in the septic tank. If the sewage system is on a city system than you should be safe but I would check with the water and sewage department if you intend on dumping a lot of slurry down the drain.

FYI Organizations such as OSHA and the EPA are starting to crack down on the dumping of material such as marble slurry. Several companies manufacturer portable slurry filters that separate the slurry from the water.