As it happens, as briefed by BAE, the BAe 146M is the designation given to a civilian aircraft that has been converted into a military airlifter.
More spin from 't Bungling Baron to pretend that they actually sold the BAe 146M.....
Anyway, to answer the original question (again), a BAe 146K would be an utter waste of effort. High maintenance costs (5 x APUs), very little offload, single hose only - a totally useless POS in my view.
Years ago I had a quick back of an envelope look at a tanker derivative of the A321. Not terribly impressive - if a VC10C1K or VC10K4 could offer 36.3 tonne offload capability on the specimen mission, an A321 could offer 24.8T. Whereas an A310 or VC10K3 could offer 47T - and an A330 84T.