By "live" track I assume you're talking about a track with just audio, maybe a stereo mix of the song.
If that track is a constant tempo, you can go to "loop view" (double click the track or view>loop from the menu) and in the loop view select the "stretch on" which is on the loop view menu. Then you can change the tempo and the song follows the tempo change.
However, when you have a tempo map it gets more conplex as the tempo varies so when you set the tempo you have to be careful as to which segment of the song you're setting it for. Tempo changes are not applied to the entire song and the above method fails.
I haven't found a way to make every tempo segment "stretch" and then change all of them via the tempo view. But maybe someone else has?
I don't actually know how to get it to work with a tempo map, just trying to give you some things I've done to maybe point you in a good direction of things to try or look for.
I've done this a bit with old recordings from practice sessions where we wanted to use the old recording as a guide to re-recording the song. Sounds like exactly what you're trying to do. I have had the thought that doing what you're doing would greatly simplify this exercise, but I've not gotten it to work very well.
What I have done is to leave the tempo constant, at something of an average of what the overall song is. Then turn on audiosnap, and set the threshold to 100% which removes all the AS markers. Then manually add marker on the song at the 1, 2, 3, 4 beats of the audio or maybe you can get away with just 2 and 4 if there is a snare to help guide you where to put the markers. Then move all those manually to the right place on the grid, stretching the audio to fit the grid.
So with this method you're not adjusting the grid to the song, you're stretching and adjusting the song to the grid.
Another method of doing this, if you have purchased the upgrade to melodyne, is to bring the song into the standalone version of melodyne, and turn on stretch and adjust the song to a constant tempo. Export that taking note of the tempo, import it into sonar with the tempo set appropriately. Now again you have a song that has been adjusted to a constant tempo in sonar so you can use the loop view to turn on stretch and adjust the tempo however you like. Melodyne also has it's challenges and sometimes doesn't properly detect and set its grid, so if you do that you'll have to learn how to manipulate the grid and get things set in melodyne prior to adjusting the tempo. But if you got a good tempo map in sonar by dragging to the timeline, which is accomplished by melodyne in sonar, then stand alone melodyne should work well.
This is a tricky thing to do and I wish there were better ways. In sonar you can use the "set beat at now" function to manually create a good tempo map. I've often thought it would be nice to then be able to adjust/smooth/set the tempo across that tempo map stretching the audio to fit.
Maybe someone else has found a better way to do it. If so it would be great to hear from them as I too have struggled with taking a live audio recording and getting it set to the grid so I could work with the song.
gabo