Yes you may be right, scripture is a bit vague on this point.
Having said that, In
2 Corinthians 11:32–33, Paul also mentions this detail: “In Damascus the governor under King Aretas had the city of the Damascenes guarded in order to arrest me. But I was lowered in a basket from a window in the wall and slipped through his hands.” This final piece of information indicates that the local Jewish leadership had persuaded the Damascene officials to help them capture Paul.
If Paul was on the run from the Damascene King and the Jewish officials. What sounds more probable. Do you think he would of returned to Damascus after only 40 days (as you suggest), or do you think he would of waited roughly 3 years ? (allowing for the dust to settle)
I guess that would be open for speculation,