Sounds like any other normal acrylic medium with added flow-aid, which should be miscable with pigment. A quick google shows that people do this, with the problems of water-repelling pigments, and the acrylic medium drying out too much while mixing. Both seem addressed by the Schminke blurb, though.
I'm not entirely sure it'd be suitable for reconstituting dried or congealing paints. I think the former would have to be ground very fine (if I read you right) to avoid obvious grittiness, and good luck doing that with rubbery acrylic. If it's possible, I think the effort needed would just make me suck it up and buy a new pot from GW, even if the tragic loss of that whole £2.50 or whatever means my family will go cold and hungry this winter. Not to mention you'd effectively be diluting the pigment in the dried paint all over again. I'm not sure what effect that would have on opacity.
I'm no expert on the acrylic drying process, but water might be more effective with drying paints: you're replacing water that's evaporated, nothing else. Adding fresh medium will replace some water, but you're also adding a lot of acrylic and no extra pigment, which will probably reduce the opacity once again.