Google has a less than perfect record in the way it conduct business with third party installation, up to the end of 2013 they had a pretty fruitful relationship with the Babylon toolbar makers for example, before that Realplayer. Also when Chrome first started to be bundled with Avast, it wasn't an opt out like it is now. It was an opt in, "yes, install" and "no, don't install" options are de-selected, so the onus was on the user to want to install Chrome. I guess the install numbers weren't great so Avast switched to the opt out. Thus I have a strong suspicion that money is changing hands between Google and Avast.
I don't know of any instance of Mozilla paying for bundling its software with third parties, or even allowing it in any type of piggyback third party installation so it is a moot point. So they certainly won't pay for it, like what Google probably did/does. Even when the EU mandated the ballot browser box on Windows, Mozilla unofficially stated through its top execs that they thought forcing Microsoft to bundle Firefox basically went against company ethos of internet freedom and what not, even though theoretically it would increase their market share.