What are the performance drawbacks when running an Index Defrag during a Full Database Backup?
Any database operation will generate extra log that the full backup needs to capture (the Full backup contains, at least, all log denerated during the backup). However, defrag is fairly small log overhead. I would not be worried.
Is there a way to pause/stop an Index Defrag when a backup starts?
No, but Defrag is perfectly OK to stop and resume later. If you interrupt defrag you won't loose the work so far. Restarting a defrag later will continue from where it was interrupted.
I utilize Reorganize when frag is between 10 and 30%,
That is, most likely, useless. Defrag is largely a myth. Stop Worrying About SQL Server Fragmentation