Can we use witnesses generated by OpenSSL's Rabin-Miller primality test to help factorization? If I have a 2048 bit value used as the modulus for an RSA exchange, and OpenSSL's BN_is_prime() has determined that that value is not a prime, does that mean that OpenSSL has found a strong Rabin-Miller witness?  If so, if we could get OpenSSL to output the witness(es), how might that help us in the factorization of the value?
does that mean that OpenSSL has found a strong Rabin-Miller witness?


Yes, it does.


  if we could get OpenSSL to output the witness(es), how might that help us in the factorization of the value?


No, it wouldn't help; for most composite numbers, the vast majority of values are Rabin-Miller witnesses (it's provable that at least $\frac{3}{4}$ always are, but for most composites, the ratio is very close to 1).  By far the most frequent for the Rabin-Miller to claim compositeness is that the random value $x$ is a value for which $x^{n-1} \ne 1 \bmod n$ (and so you never hit a 1 or a -1 in the sequence); such a value $x$ proves that $n$ is not prime, but gives no indication of the factorization of $n$.  Now, if you found an $x$ for which you fail for the other reason; because Rabin-Miller hit a 1 without hitting a -1 first, such an $x$ would immediately yield a factorization.  However, such values of $x$ occur only extremely rarely in practice.