I see. Well to be honest I don't know if it would work with an iMac, since its monitor wouldn't expect any "input signal" as it's all packed in there, right?
Then I guess you could use a KVM switch and some kind of capture solution (ElGato, Hauppauge) to get the input from the mini, but then (and I don't know if this is good or bad) it would show up as a window on Mac OS, not really the full signal (and so at the same time you could look at both screens, since the mini's would be embedded on the capture software window). If more than one Mini then one could use an additional display switch (Monoprice etc) to connect all Minis to the same capture hardware.
Of course this solution would be totally energy inefficient, more expensive and more clutter to your desk.