before you do anything get the book out for your set up and see what the specs are. maybe you have one that all you have to do is "switch" it to a lithium setting.
I know personaly if I were you, 9 out of 10 times I would change out the charging section of your converter if it is the one that came with the trailer because they are normaly junk and just kill batteries if you leave them pluged in during the off season like I do.
if not like mentioned above they will work kinda, is it optimal for the battery , nope. would I leave it pluged in for months on end , nope but you can make it work lots of people do.
Steve