Yes. I think you will need a battery charger then to top up your batteries most nights.
You probably just need to keep an eye on the battery state initially to see how you get on. I have found the heater to be battery hungry. I have the same batteries as you. I need to fully charge them every night but I don't have split relay to assist the charge. So you may get away with a charge every 2 or 3 days (not sure).
You'll just have to see how you get on though and find what's needed for you.