Knightfall
World of Kulan DM
You can have him do that. However, he will need to run quite far and he'll have to be very careful while doing so. It would be best that he not flat out run. The stone stairway is too treacherous for that to work without Balance checks.Quinn would simply run out of range of the archers, he doesn't have any sort of ranged weapon beside the net.
The archers only found range within 120 feet, so Quinn will have to move at least 240 feet up the stairs to get out of range.