No it's not. In fact, in many cases (e.g. Philip's evangelism, my own personal experience), it took place some time after the person had come to the Lord. My only point is that we have to be careful in limiting God in how He chooses to display His power and Spirit.
I agree that we should not try to limit God. I do have a question about your statement, though, that "it (salvation) took place some time after the person had come to the Lord". Would you agree that a person is not saved until his/her sins have been forgiven?