Hales gets in well ahead of Bairstow in ODIs, seriously? Realistically, Morgan plays. So if we're going with the 4 bowlers/2 all-rounders formula, Billings and Bairstow get squeezed out. Billings makes it in if we go for the extra batsman.
Realistically, yes, Morgan will survive, even if common sense says that now is probably the moment for a change (let him compete for a place on merit, but also free up the option of competition from guys like Duckett and Vince, who have done well in their limited one day exposure, and also the next generation of guys such as Bell-Drummond). As for Hales vs Bairstow...if you didn't have Roy doing the job Hales used to, then maybe. But you do...and Hales struggles when the ball moves, and can get tied down.
FWIW, my side would be:
Roy
Hales
Root
Bairstow
Buttler (c/ probably w)
Stokes
Billings
Dawson
Rashid
Willey
Plunkett