No. You would need to take ALA or DMSA every 3 hours for say a day or less and THEN do the urine/blood test for it to show any mercury toxicity. This is called a provocation or challenge test. The tests done by allopaths for chronic/autoimmune illness are most of the time useless when it comes to find out the causes, I am sorry. Conventional medicine often is a cruel comedy and the most repeated joke is tests coming back negative and you being told you are perfectly healthy (except in your head, eventually).
The reason for this is that they are not doing the correct testing, of course, because for example mercury gets intracellular, intramuscular etc Therefore, it is ridiculous to test blood and urine for traces of mercury unless you have been exposed the same day or unless you have taken something to draw mercury out of tissue.