Will Apex have a future on Google Stadia?

I don't believe Stadia has yet set a precedent for F2P games so I don't expect it to be likely. I don't think Respawn are done with expanding the games availability though. Two things that I expect EA to be more likely to consider however:

1. EA might join the game streaming arena with their own service some time between now and the next few years. Or...

2. They might consider making some form of port for mobile devices so that they can reach a separate market.

Apex is only going to become more accessible to lower end hardware as standards rise, and current gen consoles aren't going to be current gen for much longer (assuming these streaming services don't cancel the next generation). Since the Xbox One has allowed certain games to use mouse+keyboard, this could have broader implications for the next Xbox too.

Acquiring the hardware to stream a game that thousands of people play for free would no doubt be a costly endeavour.

Also I have my doubts about streaming a multiplayer shooter. I wouldn't mind it for games played at a more casual pace but I fear the input latency could make mouse aim feel disorienting.

LASTLY I don't think such a streaming service would do much to curb cheating. That is unless they decide to separate stream users from game client users entirely. I don't think that would be a very popular way to do it.