Not really how TTS engines work. Though, what you are describing is a screen reader. A program that read the text on screen; or, to be precise, calls the TTS engine and voice of your choosing to read the text that is being displayed. Depending on how advanced they are they can indeed be made to only read selected text.
The problem is of course that for non blind users screen readers are annoying since they tend to read all the text on screen. That includes the menus, context menus when they’re opened and so forth. And they tend to restart from the start if they are interrupted. Also, most don’t really work all that well, especially the ones for non android Linux systems.