Yes, this is correct - as long as the FCC (flight control computer, either AP and/or FD) is in APP mode, it can not be deselected or other modes engaged. This is also signified by the light in the APP button extinguishing when the mode engages in both LOC and GS. It is a safety feature.
The way you did your ILS followed by a circle to land is exactly right. Use VOR/LOC and VS and then you can switch to HDG SEL and ALT HOLD for the break-off.
Alternatively you can fly the ILS in APP mode, but will have to disengage the FCC (both AP AND FD) to fly the break-off (you could engage the AP at that point again).
A very remote possibility would be to toggle the GA mode and then change to ALT HOLD and HDG SEL out of that - but that is a violent maneuver that you would not really do in the real aircraft.
Cheers, Jan