If it is simple enough to test, then you might as well do so. I don't know of any service or other mechanism that will do this test for you, but if you do then have at it. The likelihood of an attack is probably pretty slim, but the severity is pretty extreme. It's certainly worth fixing if you detect it.
Yes, any prior sessions, if captured, can be decrypted if your private key can be derived. Unless you use Diffie-Hellman to generate your ephemeral session key (currently extremely uncommon); just search for "Perfect Forward Secrecy" for information about protecting today's sessions against tomorrow's attacks.
Note that your primes are determined when you generate your key, not your certificate. Generating a key costs nothing (but your time) and can be done as many times as you please. So if you're going to test, you might as well generate the key ahead of time (or perhaps several in one go) test, and then generate a CSR based only on a "strong" key. A computer with a good TRNG (such as recent Linuxes and BSDs) is helpful here, since a bad PRNG is typically your source of bad keys.
Also, several CAs will allow you to "re-key" a certificate, which essentially means issue a new one with the original expiration date. So if at any point your key is suspect, that may be an option.