There are so many different contributing factors to how a guitar sounds that it's pretty difficult to generalise them. If you want to make your own guitar, then there's a reasonably good chance of success, especially if you follow a familiar design. Features like cutaways, and thickness changes can make a massive difference to the tone of the instrument, but if you get something which looks like a guitar then it will definitely sound like a guitar, just don't expect it to sound better than a Rickenbacker.
It's important to pay attention to the type of wood you use, how it's been seasoned, and grain orientation if you want a first class guitar. Problems you're likely to encounter are getting the neck straight, applying the frets, and installing the truss rod. I once helped a guy design and build his own guitar, he was a competent wood-worker, and we had access to an absolutely massive workshop, but in the end we gave up and had the neck professionally finished.
In short, yes it is more than feasible to build your own guitar, and many people do this as a hobby and produce some amazing instruments. But it takes a lot of time, a lot of skill, and a lot of patience! Having said that, you're much more likely to have good results if you confine yourself to building an electric guitar rather than an acoustic guitar, for obvious reasons.
Good luck, let us know how it goes. I'd be interested to see a photo diary of this one!