If you have a straight mercury problem, probably not. Hg tends to cause a retention of Cu. ALA may cause a bit of a retention of Cu as well. However if you have one of the toxins that suggest the use of Cu, then maybe. Cutler explains more in his hair test book and other writings.
Was Cu high on your hair test?
Any symptoms of low Cu or reason to think it is low?
I assume you are taking Cutler recommended levels of zinc.