I can only speak from experience, but I've never had any problems. I do rinse my prints in the drum (fill and dump), but even so, I can't imagine that anything more than a good hot water rinse is needed between prints. I only occasionally wash my drums with soap.
Even if you do wash the drum, there's no need for it to be bone dry. Filling it with water before loading the paper not only tempers the drum but also serves as a prewash. And it would only further dilute any residual chemistry if that's still a concern.
(Granted, with very large drums (16x20), this approach might be is impractical.)