The brakes will work, (assuming you have 12V feed from the truck) but the emergency disconnect brakes WILL NOT. I believe it is technically illegal in most places to tow without the battery (?).
That being said, in my case, I sometimes have a case of CRS (Can't Remember S#!t) and forget to bring the battery when I go to pick up the trailer from storage. So I risk it and tow the 5 miles home without it.
2014 Jay Flight 28 BHBE
2015 RAM 2500 6.4L HEMI, Tradesman 4x4, 3.73
Blue Ox SwayPro (BXW 1503)
Upgraded from an REI internal frame backpack and a Eureka 1/2 dome tent!