I'll leave the RN guys to comment on the MK5's ROA as I think it is different, but the Mk3/3A can certainly go a lot further than 200nm. I've done 230 a couple of times and still had over an hours fuel left when I landed.
ARCC's computer will work out which flight will get there quickest but it can't tell if the job is possible. That is for the aircraft captain to determine.