I know of no reason to suspect the 'oil pump' might fail.
Have you ever seen the insides of a chevy oil pump? they are very simple. If it has oil in it, it's self lubricating, and if it has good pressure, then it's working as it should. About the only issues I've ever heard of with a factory small block chevy oil pump, is the pickup coming out of the pump, and the probability of that in a street car has to be infinitesimal...
Run it til the oil is hot and well circulated, then drain the old oil (check for foaming or water?).. then fill with new oil.... make sure you have enough, but not too much..