So you want to have potential, unknown, theoretically possible actions, which could or could not occur, with no hint of any such request, and may or may not be in accordance with UK law to be taken into account when discussing whenever he should be nicked for deliberately, definitely, absolutely, categorically, provably, self-confessedly skipping bail?
The Chinese could send a hit-squad of crack ninjas in tutus to capture him. It doesn't mean that it gets any more consideration by the court on a basically unrelated matter.
And the answer basically is: If the US want him, they need only ask. They don't have to do anything illegitimately, they could just ask for him when the time comes, dot the i's, cross the t's and they'll likely get him. Not arresting him on an unrelated matter IN CASE that times comes is a nonsense.
I don't think you understand jurisdiction, charges vs arrest, the charges in question, the arrest warrants in question, international due process, extradition procedure, or how a court is obliged to operate within the rule of existing law (i.e. not on the basis of "this random illegal thing that has almost no precedent - note how we mention other cases where they didn't get their way - could happen by one of our legal allies who could just request him, which may be harmful to him").
Spend a day in a court and you'll see much more difficult decisions being made inside laid-down legal frameworks. This is basically a rubber-stamping exercise of the only result that could have come out of such appeals etc. There's almost ZERO interpretation available to the court here. Maybe on the issue of "amount of sunlight", that's about it. And that's just common sense, not even requiring a court to make that decision but just about anyone with eyes or - worst case - a doctor.
Sorry, but I feel the one who's missed the point is yourself.
He'll be arrested for bail, no matter what, probably charged, probably sentenced (I think they'll probably go for the maximum which is, what? A year in "real" prison?). Then after that, the SAME REQUESTS that would be made if he were freely released, or escaped back into the public domain, or whatever else happened will play out from whatever countries want him anyway.
I'd actually go for "US makes token effort to obtain him, gets bored and silently gives up". But that won't even start until he's in a UK jail, most likely. And then we'll be asking for him to serve his full UK sentence first.