After removing white hairs from my beard with electrolysis, can they be replaced with black hair transplants? (photo)

Judging from your picture your beard is a mix of both white and dark hairs. To remove all the white hair follicles would be quite some task. If your goal is to remove hair because of colour why not just use a colour to change the hair colour to match the surrounding darker hairs. There would be no need for any treatment or a hair transplant. 

Yes, you can use only the black hairs for a beard hair transplant but there is no guarantee that these hairs will not turn white