The project tempo at the time of recording will have nothing to do with the live band tempo that is for sure. Any loop you drag in will probably only match the tempo of the live performance for a bar or two at most.
Here is what you have to do:
You will have to tempo map the entire DAW session so it matches every bar/beat of the live performance. The bars and beats of your DAW session will need to line up with the live band. ie the metronome of your DAW needs to click perfectly at the end of the day with the live band performance. This will take time.
Next is after you have done this then you will be able to drag loops into the session and alert the loop to timestretch to match the DAW song tempo at any point. That way the loops will stay in sync with the band no matter where they are being used in the session.
Anything less than this amount of work will result in kaos as you attempt to make loops work with a live recording. It does depend on how even the tempo is being played live if you are just dragging a loop in hoping for the best. Obviously the more even the tempo is over time the better things weill be at the end of they day with the loops engaged.
(especially after tempo matching)