According to my understanding, oil pulling should be done on an empty stomach. Somewhere in my reading about oil pulling someone asked a question about liquids and the answer was to wait an hour after even drinking water.
I'm sorry, but I don't know exactly where I read this. It may have been a post on the Oil Pulling Forum or from one of the articles that I read on the subject. Perhaps you could ask that question on the Oil Pulling Forum now and it may be answered more clearly by someone.