Below is a link to an extensive thread on this subject. Includes real world measurements and acknowledgement from Sean of Battle Borne of the issue.
If you want to cut to the chase, after reading the OP, go to post number 70 & 81. A gentleman used his BVW Battery monitor and bluetooth to monitor current flow while driving. He saw 1 to 2 amps going from the TT to the TV.
Then go to post 84 where Sean from Battle Borne says:
"Dear SilverHouseDreams (the OP of the thread)
Your observation of the problem with keeping your Li-ion trailer batteries hooked in parallel with your tow vehicle starter battery is spot on. The Li-ion battery operates on a higher and flatter voltage curve and therefore will continue leak charge into your lead acid starter. That is why a battery isolator is imperative in this situation."
Extensive Thread on Isolating LI Batteries from TV. Even real world measured data and confirmation from Sean at Battle Born. 
