I would expect online multiplayer to be Stadia's biggest strength. In trying to stream a AAA game they are just trying to stream too much. On the other hand I am sure Stadia's streaming ability is much better than your average PS4 or XB1, so it should really shine with online multiplayer.
No because data needs to travel twice the distance with stadia, so theres input delay added onto any mutiplayer game (which are usually competitive games). (everyone wants to play competitive games without a dis-advantage,like waiting 100-200 ms before your character shoots, when you hit a button)
On local run hardware, it does the calculations and stuff on your own hardware, and sends back the results to the server.
With stadia, your actions get sent to stadia, they do the calculations and send that + all the stuff you see on screen, back to you.
This means theres always a "extra" bit of delay, when your streaming a game.
This means like nothing in alot of single player games, or turn based games ect..... but you notice it in online multiplayer type games.
If you live far away from a server, its really bad.
https://www.youtube.com/watch?v=o6pf988yFSc (watch this 30secounds into the video)
(tech journalist has like 500ms-1secound delay on inputs, ei. press a key, 1sec lateron the character does the action)