The rules do not specify, unfortunately. But I would rule that they should not. In the rulebook, the reaction phase is described as planes on 'combat air patrol' in their space and adjacent spaces. I think this would go against the spirit of an airborne operation. I'll add a sentence to the working rules that transport planes only move during the regular air movement phase - not allowed to move during the air reaction phase. Any disagreement?
Thanks for highlighting this.
Mark