Actually, swallowing tiny pieces of mercury during or immediately after the procedure is almost inavoidable, as you can't completely block off the transit of fluid, however small, down your throat during a procedure of this length. They're obviously not pieces you can see, but small particles that are carried by the saliva. Until these particles of mercury are eliminated from the body in a few days, you should not take oral chelation agents of any kind.
If it took large quantities of mercury to have a biological effect, Amalgams would be relatively harmless and none of us would be here.