Yes, I had to put the same spells on every bar that I wanted all the mages to have access to at all times. It's a cheap price to pay to put a spell on 4 bars to be able to do this though. Multiboxing from what I've found is all about the setup

I use bottom left and right bars and the regular bar, so that leaves me with 4 bars to cycle through (which is perfect for 4 mages to take turns with). If I were wanting to do this with only 2 toons I'd probably just add the 2 right side actions bars to the UI and that would leave me with only 2 to cycle through (less to setup).

You could definitely do the same trick with healers and have one button cycle heals on your healers or whatever else you wanted to do with them.