With our 2004 CRV I never needed to pull a fuse and towed for many miles for without any issues.
However, with our 2013 CRV I quickly learned it would be necessary to bypass the fuse for the nav system. The battery went dead. The CRV batteries are quite small to keep the weight down. When the fuse is pulled the 12v power outlets are dead. So it was necessary to run a dedicated outlet directly from the battery. The bypass switch and dedicated outlet solved the dead battery issue.
The OP does not state the model year for his CRV.