I assume you're speaking of black bass and tournament style fishing.
that's a loaded question that has an answer of "maybe".
How big are the fish? What's the temp in the well while on the lake, and what's the temp when they're in transport from the ramp to weigh-in site? The hotter the well gets, the more likely they are to die in transport. If the fish are big enough, no, 12.5 gal ain't near big enough. The bigger the fish the more ammonia they make (excrement), which will kill them. The hotter the water, the more active they are, the more they "go", which will kill them. If you can keep it cold, they'll slow down (fish are cold blooded). Also cool water carries more dissolved oxygen. Lot of tournament style bass boats have a large well that holds a lot of water, keeps them alive longer.
Used to, guys would put a drop or two of peroxide in the well to help keep them alive but that only works when the well is not pumping fresh water in all the time (like from ramp to weigh-in). There are tablets now.
If the well is sharp square, they're less likely to stay alive. Fish have a tendency to go to the corners and try to "get out", that wears them out quicker. Minners are the same way and that's why a lot of wells have rounded "corners". Look at a lot of the tournament style bass boats. Reminds me I need to go find me another minner bucket.
Care of the well. Wash it out so it doesn't stink. If you use a soap, make SURE to rinse ALL the soap out of the well, every drop. Then once it's dried, wipe it down real good with a clean rag soaked in distilled water just to make sure. Any chemical left in there will kill fish. There is evidence that some salt added to the well's water can keep them more lively too although I ain't never tried it. Cool water. On summer days, the well temps can get really hot, 100+ around here (125+ sometimes). Bass are going to die in water that hot. About the only thing that could survive would be maybe grinnel or maybe buffalo, and those are questionable. You can cool it with ice BUT do not put the ice directly into the livewell, I like to take a milk jug of appropriate size, fill it about 3/4 full of distilled water, freeze it and then put the entire cleaned jug into the livewell to keep them alive on warm days. Keep an eye on the jug, once thawed and the water starts to warm up, put another one in. Keep the water temp in the 60's or 70's, maybe a little warmer if the water temp that the fish came out of is hot (local lake surface temp is currently 91.1). Tap water contains chlorine and other chemicals will will kill fish quick.
Just a couple thoughts, for whatever they're worth. There's a LOT more to it, but those are the basics I learned from trial and error when I did some tournament stuff (which I will never do again).