My thoughts are:
1. I do not know enough about British policy towards captured high ranking American rebels to know if a trial and execution are likely. My guess is that like his fellow member of Congress and diplomat, Silas Dean, who was captured by the British, there would be an uncomfortable room in the Tower of London waiting for John until the end of the war.
2. With a major member of Congress captured, Congress might be hesitant to send another diplomat across the Atlantic until his safe arrival was more likely. Since Franklin was already in Paris (and thought that Adams was unecessary, and even a hindrance, to negotiations with France) I think the French allinace happens on schedule if Saratoga is an American victory.
3. Assuming that Adams is released at the end of the war, it is still possible that he could be a U.S. diplomat in Europe and then be elected VP in 1788, However, a long stay in the Tower might break Adams' health(both physical and mental) and preclude any immeditate employment.
4. An interesting possibility is that Adams is relaeased at the end of the war, returns home and is named as one of Massachusetts' delegates to the Federal Convention. Adams had drafted the Mass. Constitution and had very definite ideas as to the proper organization of a "mixed" government. His interactions with Madison and Hamilton in Philadelphia might have been very interesting indeed.
5. Assuming that Adams is either dead or not fit for elective office in 1788 but the Constitution is adopted on schedule and GW is the clear choice for President, I would say that the VP will have to be a Northerner and the most likely choices are John Jay of New York (who came in second to Adams in OTL) or John Hancock of Mass.
Your obedient servant