You definitely need a battery just to pull your TM out of your driveway, as it powers the break-away brakes on the TM in the event of a separation. Major safety issue, and also the law.
Additionally, assuming you have one of the older-style converters, there is no on-board DC filtering, and those circuits that are filtered are filtered through the battery. That wouldn't make any difference for most of the electronics in the TM, though overhead LED lights would probably have a slight flicker. I'm not sure how the furnace might behave.
To make it easier to install the batteries in my 2720SL, while standing outside at the rear of the TM, lift the bed an inch or two off the bed support arms, and slide the bed inside. Then the support arms will swing freely, and you can swing them out of the way to open the battery door. And with the bed now inside, you can stand upright, making it FAR easier to maneuver those batteries, and at the same time, not risk head injury or scraping your back against those nasty bolts on the support arms. Don't ask me how I know about this.
Dave