Legally to tow, you need a good battery, for the emergency brake system.
To run the furnace you do not need a battery, just a good 12V power source such as your converter.
I have the same furnace in my 2012. I suspect the blower will run for a 20-30 seconds then the furnace shuts down, before ignition. If I am correct the issue most likely is the sail switch, not confirming the fan is working. The sail switch maybe dead or just dirty.
I have not removed my sail switch. I thought about cleaning it a couple weeks ago. It looks like you can access it, without removing the furnace. But it is not super easy looking. My Owner's manual, state the sail switch wires are white. But mine are bright blue. From the correct angles looking through the duct port you can see the switch, it is under the fan assembly. If you have a multimeter, it is a super easy test to check, without removing the switch.
To access the switch, on most RVs you need to remove the furnace. I do not believe that is required on a 23B. With the drawer above the furnace removed. Remove the HVAC duct that is over the pump. You just have to rotate it until the tabs line up. Take your time rotating the duct. May need to try both directions. Remove the wood divider between the pump and the furnace. Mine is held in with a single screw.
With the duct and drawer removed, you can see the sail switch (with a flashlight). Look down thought the duct connection, down under the fan assembly. My sail switch assembly is white, with a pair of blue wires (OM says white). As I said I have not removed mine, but I have looked at it closely.
You need to remove the fan assembly. One screw (1/4" socket head Phillips) will be a slight challenge to get to, as it is down low, right next to the wheel well. If you cannot access it, you will then need to pull the furnace. If you have the right tools you should be able to access it. There are 3 or 4 more screws holding the fan assembly in place. There is plenty of room to pull the fan unit out. It looks like there is one more screw to remove the sail switch assembly from the furnace box. It is below the fan assembly and behind the "air tube".
You may just get lucky, and it just needs to be cleaned and re assembled. But then, it maybe dead and need to be replaced. I would not recommend bending the long probes. They are what catch a the air flow, and apply pressure to satisfy the safety circuit.
If you do not have a copy of the manual, you can view and/or download a copy here;
Error codes from page 4