Does buying thousands of apps (but not installing them) cause bloat in Android? A few years ago, Google added the ability for app developers to place their apps "on sale".  They included the ability for developers to temporarily offer their apps for free.

I started "buying" these free apps via Android's Google Play store, but not actually installing most of them.  Over the years, I have now "purchased" thousands of paid apps that were offered for free.

Ignoring space occupied by apps actually installed, will continuing this habit cause bloat or slowdowns within Android?

Is the history of all those purchases being stored locally in Android as well as on Google's servers?  Does it affect application memory (RAM) available on the Android device?
No, they are not installed on the device... Your device doesn't even "know" you purchased the app. It has absolutely no effect on your device at all and your purchase history is stored on Google servers, not your device itself. 

Your device has nothing to do with the "purchasing" of the application if you don't actually install it. You don't even need a phone to buy a free app, you can just go on any computer, log in with your Google credentials, and go to the Play Store and have the free app added to your Google account.