I have some mp3 voice overs that have the narrator's breathing in between sentences. Is there a way to run a filter to pull out just this?

Unless the pause between sentences is outrageously loud, you can probably do a passable job with Edit | Delete Silence... A little tweaking of the values should give decent results. Set the "Limit Continuous Silence" to around 1000ms or so. You'll have to play with the audio/silence dB thresholds and attack times to match your source.

Naturally, recompressing to lossy from an edited MP3 will degrade audio quality.

Using Edit -> Delete Silence is good solution but if you want to have a perfect result - work manually.