I've been doing UT on and off for over a year and I really don't know the answer to this. I face a similar problem myself though I've had my fillings out, but still have mercury toxicity as shown in a hair analysis.
I believe that mercury and heavy metals in general are eliminated via sweat and stool (via fats) and less so through urine....so perhaps if you keep up sweat therapy in saunas etc and make sure your bowel is functioning properly with at least 1 BM per day, maybe you would be ok.
If you're considering getting your fillings out then perhaps avoid doing UT until then.
You could also ask at the Yahoo urine therapy group, details below. I believe the owner/moderator has a mercury filling but practises UT regularly. Perhaps it depends on how many fillings you have.
Also if you get hold of Martha Christie's "Your Own Perfect Medicine", she talks about how to use urine homeopathically, so with it being very diluted, it's unlikely to cause any problems and may even increase your body's immune response to mercury.