Yes, leaves an oily film. The only product I found that doesn't leave a heavy film is a Si02 stainless/aluminum protectant/polish designed for the marine environment and does not leave an oil film after it dries. I use it after BKF. It will even out the finish and put a nice ceramic top coat ...
I use Stainless Steel and More from aquaarmorcoatings as it is the only stainless steel polish that has Si02 Ceramic in it. I use it after other cleaners as a top coat, it evens the finish beautifully and limits finger prints and other road film.