I have always been told by the "experts" not to run a charger while you are running your troller. They said it would burn up the board in the troller.
That being said, I used to run a battery charger on my 12V set-up (years ago). It was a 10 amp maximum rating. I had two batteries hooked in parallel (+ to + and - to -). I think it ran as long as any troller I ever owned.
The down side was I had to run the gennerator.