Backing up to Nul on an SQL Mirror
If you are complying with all the RPO and RTO requierments by having database mirroring in place, with daily full backups then there are no data consistency  issues with making backups to NUL. So the answer to your question is No. 

But (there is always a but) you are not having a secondary restore path if a full backup is corrupted and both the servers go down and your restore options are always the point in time when the daily backup is made. 

By making normal log backups and storing them for 48 hours you can restore past a single corrupted full backup which is not possible to do with differential backups.