You identified a problem with the current theory of syntax. You can also ask your question another way: Is text subject to the same syntactic relationship we find within a sentence? Which indeed many early text linguists did.
But both are wrong questions. Sentence is not a very good unit of description in language because it is an artifact of a particular kind of writing. Which is why many linguists would just stop at a clause and treat everything else as text. In that sense, any multiclausal sentences are just text and anything that keeps them together is a cohesive device (e.g. connectives, concatenation). If you look closely, the only way you can reliably identify a sentence is by the presence of a capital letter and a full stop. Even intonation patterns don't do it for longer sentences - which is why raising the pitch at the end of a really really long question sounds unnatural.
But looking at your example, you're really asking about the clause. Here you're dealing with both coordination, substitution and co-reference. There's no reason not to think of them as cohesive devices in this context, as well. People generally don't talk about the 'cohesion of a clause' but if the text consists of a single clause, it still has to be cohesive. In fact, even a text consisting of a single word has some cohesion. "There!" refers to an external place. "Duck!" refers to a situation. Etc.