I think the answer is that we don't know.
I will only consider only the classical model of computation, not a quantum one cause I'm not really experienced on it.
First of all we need to clarify something, the strongest assumption that RSA can rely on is the RSA assumption, factoring is a weaker assumption. This means that if we can solve prime factoring problem we can solve many problems including RSA. If we can solve the RSA problem we don't really know if we can solve the prime factoring problem. Something else we also need to mention is that we suppose this oracle is running in efficient space and time, otherwise it should really make that sense.
I haven't heard of any algorithm that can convert a 2047-bit prime factorization oracle to a 2048-bit one being efficient in both time and space. If you have heard of one you can mention it in the comments. Particularly, I don't think anyone is interested in solving such a problem, it is actually useless. To summarize I think there are very few probabilities that we ever discover such an algorithm.
Another option would be to discover an algorithm that would convert a $n$ bit prime factorization oracle to an $n+1$ bit one both efficient in space and time. We can prove here by induction that such an oracle would be equivalent to solving the RSA. I think that would be far far far less likely to happen because it would mean actually solve the RSA problem.
A last comment is I think such an oracle may only help only in the case of a small prime factor (for example such a weak prime factor may appear in an RSA impelmentation with multiple prime factors).