Yes, a non-runflat car comes with a pump and sealant bottle. As you say, you haven't used the spare on your Dooper, except psychologically, so why not see if the pump and sealant can work as well, psychologically? Certainly for the first few years, Mini Assistance (or whatever it's called) will cover the unlikely situation that a tyre is so badly damaged that it won't hold enough pressure to get you to a tyre repair place. Admittedly you are then trapped with whatever they have in stock, if they can't repair yours.
Let's face it, spare tyres are going the way of starting handles.
Every new Mini gets TPWS.