It does seem highly unlikely, and I have never heard of such a thing - but it just might be physically possible. Winchester drives a 12 gauge slug almost that fast, but needs a 3 inch shell to do so.
With a 3/4 oz. payload, and some very special powder, crimped down like a bank vault and using the SAAMI spec pressure limit to its fullest, you might be able to get close to 1750 fps. in a 2 inch shell. Why you would want to do something like that is beyond me.
Perhaps someone was thinking of the little 1 3/4" Aguila shot shells, but they don't produce anything like 1750 fps. Two inch cartridges as designed for English (and now Basque) guns will come nowhere near that velocity, nor would you want the associated pressures and recoil in such a gun. It would require a new design of gun to make good use of such a shell, and I haven't heard of one. Still, it could possibly exist, within the realm of physics.
Sharptail