yea they will be able to tell not only by your teeth but the scarring in your throat. besides whatever you use to help you purge leaving scars so does stomach acid. So when filling out the intake papers its easier to write it down and then write next to it "being taken care of". that way they don't ask alot of questions surrounding it.
The varnish is not used specifically for bulimia. its for anyone who is losing their tooth enamel be it from nature of eating to health problems. all you need to do is ask to schedule a cleaning with floride and varnish treatment.