Another example of the confusion that is, increasingly, arising in this area.
The most basic form of a polish is when you have no abrasive and no protection of visual enhancement. This is a 'cleanser' or a cleaner polish. I have seen a few references in this thread to 'AIO' or 'glaze' and the simple reality is that these are not the pure cleanser type. These products WILL have something else in there, whether is it abrasives, silicones, polymers or waxes. This may or may not do harm to your process, but don't kid yourself into believing that you are getting a chemically clean surface at the end!
The important thing is that your compound or anything that does cutting, will also do the same thing as your cleaner polish. There is good reason to use a cleaner polish if you are just wanting to strip a vehicle in good condition and then put on a fresh LSP, but it is pointless if you are going to be doing any level of correction. Even after a correction, the only argument you could make is that it might lift some of the abrasive residues, but a good panel wipe will do this better and more easily and will have less chance of leaving anything else (by the way, IPA is NOT a good panel wipe, it does not lubricate and you can easily put fresh marks into the paint).
A final note is these 'synergies' we sometimes read about. Let me be clear, if there is an advertised synergy, there are two things to consider:
1) Your supposed cleanser/cleaner polish is actually leaving something behind that causes the synergy (thus somewhat contradicting the concept of it leaving a chemically clean surface...)
or
2) The synergy only exists when you pay out your hard earned dollars and convince yourself of it!
If a product genuinely cleans the surface perfectly and leaves nothing behind, the resulting synergy would be between the following product and the paint, the cleaner would have no part in the synergy!