Should I stop transaction log backups during a full backup?
As you can see in this table, there is no conflict between Full backup and Log backup. They can occur at same time, and, when log backup completes, log will not be cleaned until full backup (or diff backup) completes.




  Not all administrative tasks are allowed to run concurrently. In the table below, a black circle indicates two operations that cannot run in a database at the same time.


References:  

Concurrent Administrative Operations