I have not found any of the Alinco models in CHIRP to work with the DR-635T. In an effort to add it none of the methods used by the other models returned any useful data. I tried contacting Alinco for information but was ignored.

Yes, it'll probably work with CHIRP

Of course, the first place you'd look would be the CHIRP project page. That doesn't list the DR-635, but it does list the DR-135, DR-235 and DR-435, and that might be a good sign (but clearly not a guarantee, since the hardware might simply be different). In fact, CHIRP's alinco driver has a common DR-x35 base class, indicating that they expect x35 devices to be similar enough!

The fact that you can program your radio according to the official device manual to be in slave mode for cloning is also a good sign, along with the fact that the manual specifies pinout!

Not quite sure CHIRP does much but channel programming though, and I thus don't know whether "repeater data" programming is covered by it, but I'll leave that up to your experience!

Regarding cabling, the same wiki has an entry that states that the 3pin plug seems to be common among all Alinco radios.

But it's not directly supported by CHIRP, so that's something you'll want to change

Looking through the source code, you'd want to try the DR-435 driver first, as it seems to be the most similar. That won't let you do all frequencies of the DR-635T, but that's just adding a copy of the DR435Radio class with adjusted device naming and frequency ranges to that python file, which is text editing (really, aside from copy and pasting text, no programming skills required; but you can then share that addition with the CHIRP community and become a Free & Open Source contributor – how cool is that!).