No, Celiac disease is not an allergy per se, but the inability and insuffienct enzymes and body capacity to break down gluten that is present in wheat, rye, barley, etc. Gluten is kind of a sticky protein like thing. As a result, your body kind of rejects the food you digest and you end up getting the runs. Celiac disease is an autoimmune issue, and is related to IBS, Crohn's/Colitis, etc.
After awhile, your intestines get aggravated and some people get massive belly bloat from all their intestines swelling up. Your intestinal villi (the little fingerlike projections that absorb your food) start flattening from atrophy and over decades of gluten abuse, they just kind of atrophy and don't absorb food as well. People with Celiac disease who don't know or don't care they have Celiac disease tend to have the sebbhorreic dermatitis, yeasty coating on their tongues, dry hair sometimes, and other issues simply because they're not absorbing many minerals in their food. Sometimes people with Celiac disease are super skinny, but the ones I know are really really overweight since all the hormones, insulin, and other endrocrine functions go out of whack.
I'm not sure what the cause of Paul's seizures were, but I know celiac disease can sometimes cause seizures - I think it's because sometimes celiacs have calcium deposits in their bodies; if you have some in your brain, you can have seizures. We never did really find the cause of his seizures before he died and much less so after he died.
Celiac disease isn't really fatal, but over time, if you have it bad enough, you may get colon cancer from all that damn pooping and not enough nutrition in your system.
The alternative for Celiacs is to eat starches without gluten, like rice, potatoes, corn, quinoa, amarynth, teff flour, tapioca, and sometimes pure oats/oatmeal. There's others too. If you avoid gluten, the intestines can heal itself over several months and you can absorb good nutrients again. Older celiacs who have decades of damage may not have the ability to have their intestines heal back up.
There's currently not a cure for the gluten issue in Celiacs, but I've read some promising studies that scientists are trying to synthesize some sort of material that people can take to break down gluten.
To answer your question, Celiac disease is not an allergy, but a wheat allergy is different. People with wheat allergies are usually able to have other starches containing gluten.