Afaik the deal between Mozilla/Firefox and Alphabet/Google is that Mozilla receives funding for setting Google as the default search engine. When the user decides to change that after install it has no influence on that contract.
My guess is that the deal is based on Firefox' market share, so as long as the fork identifies as Firefox by user agent, this shouldn't influence it at all.
There can be only estimations, either based on market share analysis or build-in telemetry.