It might, but I don't see the point. Do you plan on just using toothpaste, or toothpaste and sandpaper. If you use sandpaper, I would just stick with water and a drop of dish soap. Either way, try it out and let us know if it works.
hm.. might be interesting to try.
the other products made for polish usually do more bad then good.
it all depends on how easily that toothpaste comes off the heatsink and if it fills in the micro pores in the sink.
Your arm will fall off and your teeth will fall out long before toothpaste makes even a mark on your heatsink.
If you are interested in doing a superior lapping job look for Clover lapping compounds.
Not too expensive and designed for the job you want to do.