One would assume that you tax carbon across the entire value chain for any product that's to be sold within your borders.
Insofar as the atmosphere doesn't confine itself to political boundaries, it certainly seems to me like that would be the sensible way to attempt such a thing. Why faff around?
Companies that don't want to pay this tax would, of course, be free to simply not sell their products in the USA. But I doubt that every participant in, e.g., China's consumer product manufacturing industry would be able to stomach such a course of action.
It would be similar for a hypothetical sugar tax. Which, of course, the US already has something like that, but of course it's currently being used to favor domestic sugar production over international sugar production, so it's not applied consistently to all sugar. But still, I think we can see from that that it's not a question of practicalities. If we can do it for the sake of economic protectionism, then I'm sure it would also work when the motivation is to mold people's diets.
(In case I need to put a finer point on it, I'm speaking here about the feasibility of actually implementing an excise tax policy; I'll refrain from speculating about its ability to achieve its stated goals.)
Long story short, I think that this sort of thing is probably less a question of practicalities than it is a question of political will. If you have political reasons to like this idea, it's very easy to come up with motivated reasoning for why it would be something approaching a panacea. If you have political reasons to dislike it, it's very easy to come up with motivated reasoning for why it could never work.