Not likely.
The strong suspicion is that teams will be allowed to wear black (or similar) if the coloured referee kit gets adopted. This is where The FA would need to be very clear on who gets priority. I expect they will say:
* The referee should wear black, but:
* In the event of a team wearing a very dark or black kit that clashes with the referee, then the referee can change to another referee shirt of a different colour provided that it meets the requirements of the competition.
* In the event that the referee does not have an alternative colour shirt, or is unwilling to change, then the team with the dark kit must change
That places the onus on the team with a dodgy kit to provide the referee with a suitable alternative, which the ref can agree to or not. The alternative would need to be a proper referee shirt with correct badging, and not a bib or similar.
I have a friend in the know(genuinely) and this is, to his knowledge, where this is going.