No it does not.
Combat Expertise and Fighting Defensively are unrelated and albeit both provide a defensive bonus trade off for offensive capabilities. When you look closely, both are different in other game mechanics, let me explain.
1 - Fighting Defensively : Allows a -4 To hit penalty for a +2 AC Dodge bonus, you need to declare the attack or full attack action in order to use it. IF you have 5+ ranks in tumble, the AC bonus granted is +3 AC instead.
2 - Combat Expertise: Allows a 1/1 trade off between to hit bonus and AC Dodge bonuses in a granular fashion (you can choose to trade 1,2,3,4 or 5 pts if your base attack bonus is high enough). Ranks in tumble will not affect this trade off or AC bonus received in any ways.
So fighting defensively is an all or nothing maneuver while combat expertise allows you to tailor exactly how much to hit penalty you are willing to trade for an AC bonus depending on the situation...
NOTE: Fighting defensively and combat expertise are providing an AC DODGE bonus..and dodge bonus DO STACK, so you could declare both actions during an attack or full attack. So for example a character with a +5 BAB and +5 Rank in tumble could actually decide to take a -9 to hit penalty and gain a +8 AC Dodge bonus...