Cyanogen play store access If cyanogen forks off and comes up as a direct competitor to Googles version,can google prevent android apps from working on cyanogen or since both are android based all would android apps would work perfectly fine with cyanogen version of android.
Android is an open-source project. Kindle Fire works with its own store and it's making a lot of money. So no, Google won't forbid you using the Android - without Google.