The quick answer is yes. A price on carbon can drive innovation because it creates new opportunities. It makes processes that today don't look viable suddenly look viable because there's an additional revenue stream, an additional way to balance the books and to turn your IRR, your internal rate of return, to something that's attractive to finance.
How the price of carbon is introduced is probably important. If you're going to put a price on some carbon but not all of it, if you're going to apply a tax selectively, or apply a cap and trade system in a way that favours one industry over another, you may end up with unintended consequences, but in general, yes.