If there is an arc that would cause the smokes to go out, they would operate on batteries until those died. If the arc causes a fire, they smokes should still run on batteries and detect it.
If the arc causes the AFCI to trip, without starting a fire, then after a few days or weeks, the smokes will all start chirping. After replacing the batteries in all of them over a period of a few days, I think most people would come to the conclusion that the power is off.
To avoid that situation, I use the master bedroom circuit to supply the smokes. If it trips, then it's gonna be painfully obvious something needs fixed. The average Joe & Jane may take all the batteries out of their smokes if a dedicated circuit that feeds them is out, but they sure aren't gonna stand for the power being out in the bedroom.