If you don't pull the fuse, expect the battery will get drained within a few hours - on our 2012, it was about two hours, and that was while powering the auxiliary brake unit. With the fuse pulled, the battery will last for a couple of days of towing without needing a charge, also still powering the aux brake unit.
The fuse powers the entertainment cluster - radio, GPS, etc. The car will run just fine without it. Pull the fuse at the start of the trip, put it back in when you need the GPS or radio.
And make sure you read the manual about the procedure for exercising the transmission at least every eight hours of towing. We do it at the start of every day when towing for multiple successive days.
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