Checking for slave lag and consistency is something you should do either way, so definitely a good thing to get that going. Especially if you are using master-master. If you think about it, basically what you are saying is that you cannot rely on the data from your standby master being correct. If that is the case, what use is having the standby master? If you failed over and the data was out of sync, then you’d be in trouble. So once you gain confidence in your standby master being accurate, there is no reason you cannot take a backup from it.
You do bring up another good point, which is that you should always check your backups, including loading the backup on another server on a consistent basis to make sure the backup will actually load (and how long it will take) when you really need it.