Alex Hales, who was stood down by England's board after being with Stokes during the incident in Bristol, will not face charges and has also been included in the ODI squad.
Along with the other Canterbury bowlers, Stokes' figures were bruised by New Zealand batsman Colin Munro, who made an unbeaten 174 from 118 balls.
Stokes has since returned to competitive action in New Zealand with Canterbury and the European Central Bank has said it will make a swift decision on his availability once it receives confirmation of whether Stokes has been charged. He did better against Auckland on Wednesday, hitting 34 from 41 deliveries as he shook off the rust.
And following England's punishing Second Test defeat to Australia today, the need for the return of one influential 26-year-old has never been more pressing. British detectives late last month passed a file to the Crown Prosecution Service for a decision, but there has been no word since.
Lake effect snow shifts south for Thursday
West winds today will not be as strong as yesterday, but will still bring good lake effect snows in over parts of MI. We see scattered little bits of action here and there, more nuisance than anything else but it adds up.
On whether Stokes will actually be available or not, Bayliss said: " I've got absolutely no idea.
Bairstow, Joe Root, Moeen Ali, Chris Woakes and Jake Ball are the only members of England's test squad who will stay on for the ODI series. "Still waiting for the police report", coach Trevor Bayliss said, highlighting the enormous uncertainty over the star's availability.
In case the ECB Board receives a formal confirmation that Stokes has either been charged or that he will face no charges, they would convene within 48 hours to make a decision on his availability for the team at that stage. He was joined in the 12-man squad with the five players that did not play in Adelaide, plus six players from England Lions (Ben Duckett, Keaton Jennings, Dan Lawrence, Jack Leach, Liam Livingstone and Mark Wood).
In addition to Stokes and Hales, Sam Billings and Mark Wood were added to the squad that beat Windies 4-0 in the ODI series held in England at the end of the British summer. After the conclusion of the Ashes, the English side will lock horns with the Aussies in a five match ODI series.