It's not terribly unrealistic - I mean, the rural roads in Ohio were paved, but the possibility of a deer strike in an area where the road signs are little more than route numbers (that are difficult, if not impossible to find on a paper map) isn't really out of the question. Think of something approximately the dimensions of a standard street sign, with nothing on it but a cryptic 3-4 digit number. Replace 'mountains' with forests (sometimes with isolated steep grades), and I have driven through that terrain. I don't know if a GPS or a cell-phone would have had reception, because at the time, I owned neither.
With luck, you might see an Amish buggy or combine tractor chugging along on the straighter roads.
My pops runs 6 counties in PA in a utility truck for the state. He's on the border of PA and NY. It's a mix up, but once you're used to it, it's no problem at all. The deer isn't out of the question at all. I'd just hit it. My truck will survive. The deer won't. But, to be fair, I drive an old beat up 96 Ford F-150 that's four wheel drive and has a gas chugging v8 in it instead of say, a plastic and fiberglass Nissan Altima or Kia Optima, so I get it. A far more likely and plausible scenario for me would be running out of gas out in the boondocks at 11:00 at night after all the local shops and stations in the 1 horse towns have already closed down at 9 or 10.
BUT, because I know that, I'd have either a spare gas can in the back, or I'd have filled up before the places closed. If you're going to try and tell me my gas gauge on the truck doesn't work (which is also acceptably inconvenient) then I'd also tell you that I always fill up at the 200 mile mark, and when I get to 120 I start paying attention, and by 150, I am looking for a place to fill up. This way I am never on an empty tank anywhere and when I choose to fill up I still have between a 3rd and 1/4 tank.
So, in the event it's dark, and I am in the boondocks of Ohio where I have never been before, out of gas, and on the side of the road somewhere... I'm putting on the hazard lights, pulling the key from the ignition, sliding over to the passenger's seat, and using my jacket as a pillow. Gonna try and get some sleep. Either a passerby will see me, a state trooper will, or somebody will stop. If that doesn't work, by morning it's light and I can see where I am going and what's up. If I have to foot it, I will. Assuming I do, I am picking one direction... the one towards the closest town / gas station, and I'm going along it until I get to an intersection that has road signs. A traffic light or four way stop sign is what I am looking for. From there, I sit tight and wait. I will likely press the button on a sign for the state troopers if necessary / I spot them first. But if I come to an intersection with a light, I'm pretty sure my phone will have a signal. At that point I send my general SOS text message to the people who are expecting me at my destination. If they aren't there or there is no answer, again the State Police / Game Warden. One of them will be by sooner or later if enough distress calls are made.
Barring all of that, somebody has got to come upon that intersection soon enough... And that's all assuming I am still not close enough to a gas station. Sure, it's an inconvenient adventure that will irritate me to irrational vulgarities spewing from my mouth in complete sentences, but it isn't an unmanageable situation by any means.