This works for me too. For songs with vocal parts, I find it helpful to sing a scratch track before recording all the audio tracks. Sometimes the tempo that seemed right for the guitar or piano part isn't comfortable to sing to and needs to be changed. Like other people have mentioned, I like to use Tempo view to map out tempo changes throughout the song -- maybe speed up the choruses a little, add a slight pause at the end of a bridge, or slowly increase the tempo throughout the song. I just keep tinkering with Tempo view until everything feels right.
My workflow dates back to a time when there was no simple, reliable way to extract a tempo from a freely recorded audio track. If you wanted to use MIDI drums or other parts, it was easier to record to a loop or click from the beginning. I'd be curious to hear more from people who use Melodyne or some other tool to extract a tempo from a freely recorded audio track. How well does this work? Do you have any tips for getting the best results? I could see the benefit of this approach if it's workable.