No, I have never seen any tattoos on my T. I would probably be OK with it as long as it wasn't offensive (e.g. a swastika).

I am a nurse and when working at hospitals (at least the ones I have been at), we have to cover up our tattoos. All the health workers do--doctors, nurses, dieticians, therapists, etc. It is considered part of the dress code. You can buy arm bands in various sizes and skin tones to cover up your tattoos. If you have tattoos on your hands or face, I don't know what they would do. Of course, therapists based in outpatient clinics or in private practice have a lot more leeway in setting their own dress code.