The disruption normally does not last very long. The biggest issue is usually the motorcade route; no other vehicles will be allowed on the road as it passes, so if your route is between the airport and the venue where he will be speaking, take that into account. You could encounter a highway detour or roadblock on your way to the airport, though it isn't especially likely.
Nothing that happens inside of the passenger terminal changes when AF1 is coming in. You would board the plane at your scheduled time, but you might not take off on time. What happens is that there is a brief ground-stop starting when the tower is notified that it is on approach; all planes are held on the runway from that point until AF1 has landed and taxied to the unloading point, which is always WELL away from the passenger terminal. The POTUS and his detail usually deplane pretty much immediately, and once the motorcade leaves the airport grounds, then commercial runway operations can resume. They have it down to a science; usually the ground stop lasts no more than about 40 minutes.
If he is speaking at about the same time as your flight departs, you probably will not have much trouble, assuming that you arrive at the airport 90 minutes before your flight. You should be getting to the airport before the motorcade rolls, and he will already have left the airport when you are scheduled to depart.