Can a laptop cause an AFCI to trip?
1)
According to NEMA Florida has adopted the 2008 version of the National Electrical Code. The 2008 version requires AFCI protection on all 120 volt 15 and 20 ampere circuits supplying

Family rooms
Dining rooms
Living rooms
Parlors
Libraries
Dens
Bedrooms
Sunrooms
Recreation rooms
Closets
Hallways
Or similar rooms and areas


National Electrical Code 2008
Chapter 2 Wiring and Protection
Article 210 Branch Circuits
I. General Provisions
210.12 Arc-Fault Circuit-Interrupter Protection.
(B) Dwelling Units. All 120-volt, single phase, 15- and
20-ampere branch circuits supplying outlets installed in
dwelling unit family rooms, dining rooms, living rooms,
parlors, libraries, dens, bedrooms, sunrooms, recreation
rooms, closets, hallways, or similar rooms or areas shall be
protected by a listed arc-fault circuit interrupter,
combination-type, installed to provide protection of the
branch circuit.


2)
I'd assume the laptop is not powered directly by line voltage, and that there's some form of electronics between the wall and the laptop. This circuitry should be enough to stop any noise from reaching the breaker. Though it could be something in the circuitry that is causing the problem, if it's not functioning properly.

3)
You didn't mention whether you're unplugging the laptop from the charger, or the charger from the wall. Unplugging the laptop from the charger, should not cause any problems with an AFCI. Unplugging the charger from the wall, could generate a spark (arc) which the AFCI could interpret as dangerous.