In my opinion, I don't think it matters much if you're just driving from the LFS to home. It would matter more if you were shipping overnight as eels produce lots of waste, which isn't good in a small, closed environment like the shipping bag. If you see it eat, I'd go ahead and take it home.
That being said, it is very important to properly acclimate your eel to your water conditions and temp before adding it to your tank. It's also important to give your eel some tubes to call home. When I added mine to the tank, I guided him into the eel tube as they are nearly blind and I didn't want him hunting around and stressing himself out trying to find a comfy place to settle in.
I didn't actually witness my eel eat before purchase, but the LFS I got him from is reputable and I spoke to the eel-lover there who personally oversaw his care. I made sure to have in my tank the foods he was known to be eating in the store (ghost shrimp) right from the start. If your LFS is having success feeding something else, buy that from the store and take it home with you.
I can imagine that shipping to AK could be daunting, but I only had to buy one lot of 50 marine ghost shrimp. That was enough to get my eel settled in and eating happily, and bought me enough time to slowly and comfortably get him transitioned to frozen food. I wish it weren't so expensive to get more as it is totally cool getting to watch the eel hunt them down. Time and time again, the biggest complaint I've seen from people who want to have predatory fish (eels, lionfish, anglers, etc.) is the cost of providing them a diet of live food, especially if they can't transition to frozen. If you want this type of animal, you have to be prepared to spend the money to provide an on-going diet of whatever they will eat, no matter what that may be.
I have a mandarin that won't eat anything but pods (not in the same tank as the eel). Doesn't matter what I offer, even live adult brine shrimp, BBS, mysis, whatever. He won't eat prepared and he won't eat any other live foods. So, I have to make sure I have a steady supply of pods, which usually means buying a container of them every month at the LFS ($20/month) to ensure my population stays healthy. You can't count on your ability as an aquarist or the animal's appetite to reliably make them eat the food you want to give them.
Also, I didn't QT my eel. Getting them settled into any tank is difficult enough, so why make them go through it twice by going into the QT and then the display? Any meds or hypo you might do in QT would just make settling in that much more difficult for the eel. It's my understanding that eels have increased immunity to diseases like ich due to their thick slime coat. I have two skunk cleaner shrimp in my tank with the eel, and I've seen them cleaning him once or twice, so it was a gamble I took. Not to say you should go one way or the other on that, just relating my experience.
