Scott,
Slime ain't as bad as fix-a-flat. It's just messy. It might get gummy but certainly doesn't doesn't get 'dry'. As long as you forwarn them, they are usually pretty good about it.
Fix-a-flat on the other hand is flammable. If you don't do it yourself, you should warn them to deflate the tire outside. If you deflate it yourself prior to taking it in for repair/replacement, remove the needle valve (don't just press in on the valve - it'll get gummed up & never work right again).
Best bet - tell them "my buddy Larry borrowed my VX & got a flat - he put some of that Slime stuff in ..."