I suspect it probably will, but the drain will be very minimal. I had a similar situation and installed a power outlet in the floor near (under) the seating area and plugged the Pronto PSU adapter in and run a line to the stand. Ergo, it is always charging where I use it.

I cheated in that I just ran the power (18 gauge Zip cord) to the seating area uder the rug after notching out the underlayement. Installing a conduit and outlet was just too much work. The power draw is very low and I probably could have used a piece of 300 ohm flat cable and not notched out the underlatment.

Eventually I may change the seats to motorized recliners at which time I will run the coduit and do it right.