Indeed I wonder why not. I updated the info for my old Convertible so it said 2 door.... on the V5, not dificult, and they never asked any questions, same when I changed the engine, registered the new number on the V5, you need to be as legit as possible these days.
I would say the roof is the most important consideration in any of these conversions, a good / bad soft top can make or break it really. I had no roof at all for about 5 years with mine, only used on sunny days and carried a tarpaulin just in case. I later had to make a soft top when I had to use the car as the daily driver, but it was pretty ugly to say the least and not a 2 minute job to take down / put up.
That's one of the reasons I'm considering keeping my car a coupe rather than a convertible, until I'm sure I've got a perfect soft top solution. (Preferably powered too !)