No. The drugs aren’t on the hair.
They’re in it. Drugs travel up into the hair shaft from the bloodstream. So dyeing and bleaching, and even washing, will lower any medicines that have become deposited on the hair (again, perhaps from second-hand exposure), but it will not remove the drugs that are actually in the hair shaft.
Before drug testing, in any case, the hair collector will wash the test subject’s hair to make sure that any drugs that show up will be from the hair shaft.