Logically, the fact that the two stays do not fully overlap should be of no relevance, because for a period of three nights there will be two occupied rooms recorded under your IHG 1R membership number (and honestly, it should also does not matter if this is in the same hotel or not - you should only be getting the program benefits for the room in which you are physically sleeping).

However, that is only the theory - there is no telling how sophisticated their reservation system is in practice (I mean ... this is the company that suffered one of the greatest security breaches in history for using the password "Qwerty1234" to protect its systems ...).

I am personally not aware of any real-life expereinces reported here or across the major blogs - but let's be honest, if such a loophole were to be once available, the likes of SF, LL, etc. would have stuffed it been all over it long time ago it and would have destroyed it for everyone else.