As you said, the supercharger is always spinning so you got a component that absorbs power all the time, so that's the reason it'll have less MPG than the same engine without the SC, even "off boost".
Obviosly when the SC is working you get the MPG of a much more big engine as you use more fuel with the compressed air, plus there's still the mechanical resistance of the SC.
With "off boost doesn't exist" I mean there isn't an engine speed or a specific quantity of gas that gets the turbo working, with a turbo you can drive under this rpm "limit", driving "off boost", and even when you floor it the car doesn't go anywhere and you get good MPG. If you do the same with a SC, the cars pulls at every revs and it's always on boost, even if its a boost depending on how much rpm you got.
Anyway, the Pentagon engine is not very sofisticated (it comes from the Chrysler PT Cruiser), it has 16 valves but only 1 cam, no vvt or other gimmicks.
It's strong and reliable and very tuneable but not economical to run!
Even the 115 cv Cooper struggles to reach 12 km/l with normal driving (I had one and I have better MPG from the Clio!) The Cooper S usually is around 9, the JCW/GP 8 or less.