Welcome to the forum!
Congrats on getting a "new" HiLo, you are now a part of a special community of HiLo owners. We are a friendly bunch and always willing to help each other.
About your fridge, you can run it while on the road ,but there are a couple things you need to keep in mind. If you run it in the DC mode, which is preferred, you had better have a good charge line from the tow vehicle and a good battery. The fridge draws about 15 amps and can drain the battery easily. Although not recommended for safety reasons, many run their fridge in the LP mode. If you stop for more than an hour either raise the top or turn off the fridge because it won't be properly vented while sitting still.
If you have everything cold and the fridge started the day before you leave, you can keep the fridge turned off and travel for several hours with no problems. We do that most times.