Depends on how it would be applied, but in the long run I think so.

The thing is that Bitcoin does not increase carbon emissions directly, like, say container ships or factories. There's hardware that needs to be produced and shipped, sure, but a big part of Bitcoin's carbon footprint is its electricity usage. At least the part that is drawn from non-renewables.

Accordingly Bitcoin miners would get hit by a carbon tax almost exclusively indirectly, that is by an increase in price of non-renewable energy. Now this may lead to miners that solely rely on non-renewable energy winding down their operations, however this only means that those mining operations would get replaced by more ecologically sustainable ones. Mining will always reach an equilibrium and if it's an (almost) carbon neutral one, all the better.