You can probably get away with a slow detox using small amounts of dietary supplements (not DMSA or DMPS), whilst having mercury fillings.
How well you detox will depend on how efficient your main eliminating systems, liver, gall bladder and kidneys are working.
The liver and kidneys are not like a rubbish chute were toxins and metals are automatically dumped no matter how much they are forced to handle. Some people are poor eliminators due to genetic defects in the enzyme systems, or poor cellular methylation, causing inadequate glutathione production necessary for increased detoxification.
In these instances its necessary to get the liver and kidneys working as well as possible to avoid the scenario of binding more metals than the detox system can readily handle and the supplemental chelator being forced to drop the heavy metal in some organ like the brain when the chelator life runs out.
In the case of Alpha Lipoic Acid (ALA), the life is 3 hours and this is why children with autism(who have poor elimination)who are undergoing chelation, have low doses of ALA (35mg) every 3 hours to ensure that there is not more bound mercury recirculating than the detox system can handle. If you have average liver function you can probably get away with 100mg ALA in an 4hr time period. The Jarrow Liver PF supplement has this dosage.
The watchword is low and slow with mercury chelation and a high protein diet as well as adequate intake of vitamins/minerals.