Of course, that's exactly how it works here, else than your handling of old mums. Mums which have been cut back several times will flower copiously with many bud sites and will be very bushy. Each will occupy several times the usual space of the 'lollipopped' plants, so be ready for that.
I find that after about 6-8 weeks of providing cuttings, my mums are losing vigor and may have picked up some gnats in the rootmass or their general weakness may make them more susceptible to powdery mildew. Instead of flowering my old mums, they go to the compost. Their rootmasses and old media go to the rubbish, along with any problems they may have acquired in their selfless service to the cause.
This prevents problems being introduced into the main flowering area.