I have a selection of large MT2-3 HSS drill bits that I would like to shorten (to remove the MT) and turn down to approx 13mm diameter to fit in my lathe tailstock chuck. Is this feesable? How easy will the material be to turn on my lathe?
Geeezzzz, that's an awful waste! Why not get a adapter sockets to get from your present tailstock to MT2 and MT3? That way, you'll have the best of both worlds. Silver & Demming bits are also available fairly cheap today, but those MT2 & 3 will most likely be quality tooling and quite useful to others if you wish to sell.
If it is MT-3, then you use the larger bits directly in it, and use the smaller ones in a MT-2 to MT-3 adaptor sleeve. This will give you less projection (which eats distance between headstock and tailstock) than the modified bits in a chuck large enough to hold them.
If it is MT-2 -- use the smaller ones directly in the tailstock, and use a step-up sleeve to fit the MT-3 drills in the MT-2 tailstock ram. This *will* eat distance -- but will still be better.
Large drill bits with reduced shanks tend to slip in chucks. You can buy them in sets -- called "Silver & Demming" bits. (I'm not sure of the spelling of the second word.)
If your tailstock does not have a Morse taper at all, I guess that you will have to do this, but plan on setting up in a milling machine with a dividing head and milling three flats on the reduced diameter shank at 120 degree intervals to help control the slip -- at last in the drill chuck's jaws -- though it may still slip at the Jacobs taper fit from the arbor to the drill chuck.
And while the working end of drill bits tends to be hard tool steel of some form or other, the shanks are usually a much softer steel. Just look at the shanks of bits which have slipped in drill chucks -- they will be grooved and there will be parts projecting up which have been wiped. And if this happens in the smaller bits, just think how likely it is in the larger bits.