Can having arthritis in your c spine effect placement of an epidural?

Yes. Although an epidural needle is placed between the bones of the neck it there is a lot of deformity from the arthritis, this can make the "target point" of the injection more difficult. The standard of care for doing a cervical epidural is to do it with some type of radiologic guidance, typically an xray device . A well trained specialist will not perform it if he/she deems it too risky.
Maybe. I assume you mean an epidural steroid injection. An experienced specialist should be able to inject the steroid under x-ray guidance even if you have arthritis.