Sure, if you choose to buy from the polluting producers. The point of the carbon tax is that they now have to pay for some of the cleanup. The externalities that their pollution is causing that they are not currently paying for. It doesn't limit the pollution as much as a properly done ETS would, but that's for the future. The point of the whole carbon tax thing is that it now means that the things that appeared to be cheap because they were dirty, but weren't cleaning up their mess, are now equivalent in price, or close to, those things which are not nearly as dirty or polluting. So, if two things are now equivalent in price, and one is a dirty technology and one is a clean one. Which will you pick to spend your money on?
I know which I will. I'm already choosing cleaner technologies where I can.
Since the tax is combined with some compensation for those who do not have high incomes, it will mean, at least for the short term, that people will be able to choose cleaner sources who have not been on a level playing field up until now.