In Appalachia? Don't count on it.
Almost 20 years ago, we tried to find a Catholic priest to officiate at my great-aunt's funeral. One of the two priests in Northwest Georgia couldn't make it, because he was presiding at the funeral for the other. We had to settle for an Episcopalian, explain the situation, and ask him not to wear a wedding ring. We didn't burden the widower, a 90-ish man who'd had a stroke, with any of this information.
With the influx of Latinos to work in the carpet mills, I'm sure there are more catholic churches now, but finding an English-speaking priest might still be a problem.
My daughter lives in a suburb of Richmond, VA. The new Pastor of hercheurch was transferred from a "circuit" in Appalachia. I think he had 7 Catholic churches under his wing -- most of them in the 200-400 parishioner size. Perhaps even less. He traveled from parish to parish over a wide area to say Mass, so I know what you are saying.
Actually, I wanted to say that it was probably impossible to find a Catholic clegyman on short notice PERIOD. But I was sure that some other FReeper would jump down my throat, so I just conjectured that they hadn't thought of it, or hadn't tried hard enough.