There are a few restrictions on who and how ICUS can be conducted.
1. The person doing the ICUS must hold at least an CPL, an endorsement on the aircraft that would let him/her fly the aircraft as PIC and any rating(s) that are required for the operation, i.e. Instrument, sling, etc, etc.
2. The person doing the ICUS is the co-pilot of the aircraft. (does this have implication as how you log the time in your log book, see below)
3. The operator of the aircraft permits the person to fly as pilot acting in command under supervision.
4. The PIC (the person supervising) is appointed by the aircraft operator.
So the requirements of CAR 5.40 do not allow the holder of a PPL to receive ICUS and the person conducting the ICUS must also hold at least a CPL.
If the person acting as pilot in command under supervision must be the co-pilot, it then follows that he/she would have to log the flight time as co-pilot.
CAO 40.1.0.8A and CAO 82.3 just states what minimum aeronautical experience a pilot conducting certain operations, e.g. PIC under the IFR (82.3.4.1(b)) or PIC of an aeroplane above 5700 Kg (40.1.0.8A.2(a).
The CAR states the circumstances under which a pilot may fly an aircraft as pilot in command under supervision.
CAO 40.1.0.10.7(b) seems to contradict CAR 5.40 (1)(d), but one could argue that the CAR applies to CPL and the CAO is a concession against 5.40(1)(d) to ATPL holders as it specifically mentions ATPL holders or does the CAR overrule the CAO and CPL and ATPL holders can only log co-pilot time? If they act as co-pilot hjow can they log ICUS.
An example of the CAR and CAO at odds, see CAO 29.5.7.1(a) and CAR 157(1)(b).
Can any one show where P1 and P2 are defined in the CARs/CAOs. Suggest we stay away from the overseas definitions.
As to the type of operation, private, aerial work, etc. the CAR does have any requirements or limitations so ICUS may be conducted on a private flight as an aircraft conversation may conducted on a private flight. As long as both pilots have at least a CPL, ratings as required and the operator approves.