Balancing an A/C is all about aligning the centre of mass of the A/C with the centre of lift of the wing. If the CG is too far back, the A/C is fundementally unstable, and while it can be controlled, it requires continuous control input. Modern military A/C and some high performance sports A/C operate in this mode. If the CG is forward, the model is more stable, and can be trimmed to fly without control input. Generally the required CG point is somewhere in the range of 25-30% of (weighted average) chord, which gives a suitable compromise between stability and controlability. Trimming is not an exact science for model A/C - much depends on model type, and performance preferences/abilities of the pilot.
The mass of propellor and spinner are at the foremost extremity of the A/C and therefore have a substantial moment arm. Even a small mass here will have a significant impact on CG position. The mass of propellor, spinner, nut etc MUST be taken into account in CG measurement and/or calculation.
Another significant variable is the impact of fuel tank contents which can vary by several hundred grams from start to finish of a flight. For most A/C it is impractical to locate the fuel tank on the CG so the best practice is to balance the A/C at the designated point, with the tank empty. With the tank full, the CG then moves forward which makes the model more stable.
It should be remembered that CG is a three dimensional situation. A high wing A/C can be balanced simply by holding under the wings, but for a low wing A/C, while a balance point may be found, this will not be a stable position and the A/C will tend to tip forwards or back. A better way is to balance from hard points located higher up on the fuselage.
If your advisor recommends balancing without the prop, then the rationale is that he prefers the responsiveness that a rearward CG position will provide. He is obviously a sufficiently competent flyer that he is happy to forego the potential loss of stability. Ask him to fly with 100grams of lead in the tail and you may get a different answer!