I do the same, but I would not call that "wine" after a few days. It's effectively vinegar-in-waiting.

If kept at room temperature, sure, but it will take a good few weeks in a fridge.

Indeed, it's a matter of perspective. I don't touch the stuff to my lips, but it's a great reagent

I use wine to do the same, but I just finish off the bottle. Also get no complaints.

How much does it accelerate caramelization?

The alcohol is great at dissolving sugars that are stuck to the pan -- by doing so near the burning point of sugar, you "rescue" the sugars from burning to carbon, et voila, caramelized sugars. Further, the steam breaks down the cell walls, freeing delicious juices for caramelization and breaking down the structure to improve heat transfer. You can get there low & slow, or you can add a few well timed splashes on medium high for nicely caramelized onions in minutes. It's a threshold game, and the closer you come to burning the pan, the darker onions get. Contrary to the sibling comment, I prefer white so I get clearer feedback about that threshold.

That's super good to know. Caramelizing onions takes forever

Red wine makes it look darker. Also, you may need some liquid to loose the onions from the pan that would burn otherwise (deglazing). So using red wine allows more heat and optically gets you there faster.