Right off the bat, here's an easy way for you to try it out: the Squier Vintage Modified Thinline guitar, in Shoreline Gold, is 24.75" with an otherwise-normal Thinline Telecaster body. They're not being produced right now, but you may be able to find them still sat in some shops. That will give you a good idea of the feel of the combination. Do be aware it has a 7.25" radius fretboard and obviously has a semi-hollow body, though. Also note that there are other Vintage Modified Telecasters, including other Thinlines, which are
not 24.75" scale. The 24.75" Thinline is easy to spot because it only comes in Shoreline Gold, and none of the others do.
Now, as far as experience with conversion-necked Teles goes, I've made six of 'em for myself, with a varitey of pickups and wood combinations from totally classic to bizarre—I'm finishing off a scrappy Tele-Les Paul hybrid right now—and I've put together a few friends' 24.75" Tele builds, as well. I've even swapped parts around between the guitars, so I've covered pretty much every combination possible, at one time or another.
[If you want to skip my in-depth commentary and get straight to the point, skip down to the bit begining 'tl;dr'
]
In terms of feel, you're obviously mostly getting the Gibson side of things. With the normal Tele bridge (or other Fender-style hardtails with block or bent steel saddles), you will notice a little more resistance when bending strings a full tone or more, compared to the common Gibson tune-o-matic and stopbar. Because of this, and the increased tendancy towards buzzing as your shorten the scale length, I highly recommend you go for a fretboard radius of 11" or more. 11" is the smallest radius I've tried with this kind of neck on a Tele and been able to completely avoid buzzing when bending. The common Fender 9.5" radius, with the shorter scale, is hard to get playing well without buzzing when bending; the 7.25" radius, as found on the Squier VM Thinline, completely frets out unless you raise the action very, very high. Compound radius fretboards which end at least at 12" should be totally fine.
Personally, I prefer a straight 12" radius, regardless of the type of guitar, scale length or bridge, so that's what the majority of my conversion necks have and they play absolutely fine. I also like really round and really thick neck stocks, so most of mine have actually been thicker than Gibson necks; I typically aim for around 0.87" at the nut and 1" at the 12th fret. Obviously, having a 12" radius fretboard and a rounder-than-normal neck helps get away from the normal Tele feel. (Unless you compare it to an original 'nocaster' Fender Tele, which have necks thicker than 1" all the way through!)
As far as the tone goes, I have not noticed any differences which can be put down to the scale length. There have definitely been changes as I've experimented wih different wood combinations, but those have always been in keeping with what I expected; mahogany and rosewood sounds much warmer than a normal Tele, while ash and maple sounds exactly th same as a normal Tele. The hotter/warmer the pickups get, the less and less I notice a difference, even with very different wood and construction combinations. For reference, a SD Hot Rails tele-size humbucker, in a semi-hollow Thinline body, with a 24.75" all-rosewood neck, never sounded much different than when I put the same pickup—not another of the same type, but
the exact same pickup—in a solid alder body with a 25.5"-scale maple and rosewood neck. Same bridge, same electronics transplanted. Very different guitars, but virtually identical sound when a thick-toned humbucker was used. On the other hand I've tried similar build comparisons using standard Tele single coils and the differences becomes a little more apparent.
One thing to remember, when referencing Billy Gibbons' most recent Tele, is that his is only lightly chambered, the neck is an unusual mahogany back and maple fretboard combination, the neck is set in with a long tenon, the pickup has been specially tweaked for it, and he uses .007 strings. It'd be easy to make something along the same lines as that, but it'd be hard to really copy it fully, and it'll never quite sound the same.
tl;dr:
If you're using the Gibson scale, Gibson fretboard radius and a Gibson-esque back profile, it'll feel like a Gibson. You might notice a slight difference when bending strings, but it's not much of a change at all, and many people won't notice it. You could of course use a tune-o-matic and stopbar bridge to complete the Gibson feel.
If you're using a powerful humbucker, it'll sound just the same as if you put a similar pickup in a Flying V, Explorer or SG. If you're using a lower-output, brighter humbucker, definitely make sure you use a mahogany neck and a weight-relieved or chambered mahogany body to complete that tone. I also recommend using a 300k volume pot and 500k tone pot, instead of the common 500k + 500k set up. Neck pickups are a different case, but it sounds like you won't be using one of those anyway.
