Thanks for the responses.
The reason I asked is because I slacked off on the amount of soap I was using since I decided it might be best not to strip all the oils off the steel during cleaning. I also rinsed after cleaning in the soapy water, like all the poll respondents so far do. Then I began to wonder.....
My parts out of the mildly soapy water were already nearly dried by the time I finished cleaning them, and the soap wasn't leaving much, if any, visible film on the steel. So, why, I wondered, do I really have to re-subject the steel to further wetting? Does the little bit of soap left on the surface neutralize the oil I apply enough to worry about? Would a soap film cause rust, or prevent it?
Those are the reasons for the question. Any thoughts?