Hi Richard
That's great that you are getting to be part of a CoE. It means your company is trying to take the support environment serious with a standard. Yes, it is an example of moving from business background into SAP via support.
I had a chuckle when you mentioned that book. I bought the same title (though methinks 1st edition) about 10 years ago when I was at university and wanted to know all things SAP. I also bought SAP for dummies and a few others). I love my books, however there is a heap of other content out now.
If you are trying to prepare yourself for your future role then you might want to obtain a free SAP Learning Hub Discovery Edition Account (go to training.sap.com or SCN Training space for information). You can then get access to free course content (full subscription costs the equivalent of a 3 day training course but gives you all SAP course material). Anyway, the Discover (aka free version) does contain a few business process overview and getting started courses. At same time, you might find it worthwhile to invest in the full version.
Getting a functional background (i.e. MM) with GRC can be quite useful. End of the day, a large part of GRC is risk management. Within Access Controls you have Access Risk Analysis which is about segregation of duties and mitigating this risk. If you know the module and the processes then you will be in a better position to interpret risk. Process Controls is another section (I have little experience on).
As you are joining a CoE you will get a lot more hands on training and have a better chance of finding your way through experience and opportunity at the time. You will also get system access which will make learning a whole lot easier!
Good luck with it all