Is it possible to put trim on a guitar after it's been built, and still make it look neat?
Yes, but you'll probably need to do a refinish unless its an oil finish. It depends on the radius of the round-over on the edge you want binding. If its a bolt on, its a lot easier too.
Well, is it hard and shiny, or does it look like the wood itself is coloured, and the colour wears off over time?

And, waht kind of guitar do you have? Oil finishes are pretty uncommon these days.
Enjoi <--- Friend me
Quote by Scowmoo
Otter, you're my new god.
It's a Squier Tele in butterscotch blonde. It says it's a polyurethane finish. What difference does that make?
You'll have a job in that case coz when you rout the channel it'll chip all the paint. Then you'll have to finish over the top of the binding so its protected and blends in with the other finish. If its a Squire it might be worth a go just as an experiment. You can pick another quire body up really cheap. or buy a cheap body to practice on first before you have a blast at yours