I was going to ask that exact question.
I think the answer is no, they can't stop you. And perhaps I'm being naïve, but it doesn't seem like it would be too terribly tedious if you used a scraping library, at least not for replacing basic API functions (i.e. getting a user's recent tweets).
Obviously this would be limited to public tweets (no private tweets, no tweeting on the user's behalf, and no DMs).