I think it will do OK, but biggest problem for Stadia will Microsoft that will offer something similar but with better offer of games.
XBox vs Stadia promises to be a very interesting console war to watch. XBox is yet to fully unveil their hand at this point, but they could certainly put pressure on Stadia early on thanks to actually having a userbase with dedicated hardware already. Though there is always the fear of both systems ending up acting as a harmful oligopoly, both offering the bare minimum and not compete at all between them.
You know it deserves the GOTY.