Yes, this makes sense. The answer is sort of.
On my Apple TV 4K, it more or less works as you describe. If I close the Plex app while I’m viewing the guide, the next time I open Plex it starts at the guide. That is, as long as the app is still running in the background, it remembers where you were. However, if the application is stopped (forcefully, or do to some background reaping process), the next time it is opened it will start at the home screen. The same is true of my Roku Premiere. I don’t have an Android TV client handy to test with, but it is likely the same there as well.
However, there is no setting to have your client start in a particular library/section of the interface. The behavior above is just a function of the fact that the app is still running in the background so, when re-opened, it just picks up where it left off.
Having said all that, there is an existing feature request to have this functionality (open straight to Live TV & DVR); however, it doesn’t seem very popular:
