If you're really thorough about checking maintenance items like tyres, it'll probably be fine. If you're more happy-go-lucky, then maybe not.
I used Slime for one set of tyres, and never had a problem with tyre fitters or stability (VFR 750), but to be honest I'd rather know when I've got a problem with my tyre than be riding around blissfully unaware.
Regarding the tyre fitter comments - is it Slime that they don't like, or the emergency squirt-in latex stuff. I'm sure that would be a right faff to clear up.