Depends. In the first place, you're going to levy a pigovian tax on the electrical production. That eliminates the negative externality as Bitcoin doesn't necessarily affect the environment directly. The cause of the negative externality is primarily the production of the electricity.

Now, it could be great for Bitcoin as you're going to have lesser people arguing that Bitcoin produces too much environmental pollution as the negative externality is accounted for. This doesn't necessarily means that the act of mining doesn't affect electrical production but it is bound to drop given an increase in the cost, -ve externality being internalized. Same can be said for any other activities that requires electrical consumption.

It could be bad for Bitcoin as there are now lesser miners, which affects the security. Forcing miners to certain kinds of energy can be potentially detrimental to the community; if the government doesn't regulate the electricity, then miners would be using far too much electricity from a certain source (which doesn't have carbon tax) and thus negatively affect the community around them. I doubt this would happen, electricity market is often regulated with the local government.