No, nyet, never, nunca....
BMW does not need to "get Mini owners to move to an M1"... There will be enough takers that they would never need to do that. Also, BMW would not, at least consciously, promote an intrabrand rivalry.
People will "move" to the M1" if they have the cash to do so, if they really love the car, if they have a need for speed.... oh heck... there are a plethora of reasons one could come up with.
It is more likely that an M1 owner might supplement ownership by having a Mini to drive when the "M" is in the shop.
M-cars are special as we all know... but so are MInis... for different reasons. Even a small-ish M-car is going to be vastly different in character from the Mini. Each has its own allure.
My 2 cents...... deposited.