My thought on it is that yes, it can work - but it may not turn out how the player wants.
Whirlwind Attack + Great Cleave - say Joe Bob Fighter has 4 attacks per round. In front of him is a pit fiend. On either side of Bob are 2 goblins. Now, with Whirlwind attack, Bob could make one attack against each guy, and if one drops, he gets an immediate Great Cleave against an opponent in the immediate vicinity. (As per the FAQ).
Since using normal multiple attacks doesn't require you to declare all attacks before you roll the first one, I'd figure Whirlwind attack works the same way (It doesn't say differently, and in all other ways each attack in the Whirlwind is treated like a normal attack). So Joe Bob decides he'll work right-to-left.
1) Hits Goblin 1 for 10 damage, kills it.
2) Takes his free attack from GC on the Pit Fiend.
Wait, what about that goblin in the middle? Imagine how a Cleave would work. Weapon goes through the first victim, then on to hit the second. The interposing goblin may provide partial cover for the Pit Fiend, or possibly a penalty on the Cleave attempt.
Anyway, Joe Bob kills the second and third goblins, each time taking a Cleave attempt on the Pit Fiend. Attacks the Pit Fiend, no Cleave (doesn't drop it). Attacks the last goblin - and it doesn't die.
Next in initiative - the goblin, who has quite a few levels in Cleric. He casts Raise Dead on one of his buddies. Raised Goblin gets up.
Next in initiative - Pit Fiend, who coincidentally has Whirlwind Attack and Great Cleave.

What, demons can't learn nifty combat tricks?
Pit Fiend attacks the raised goblin - kills it, WHACKS Joe Bob with his cleave. Attacks the goblin cleric - kills it, WHACKS Joe Bob with his cleave. Then attacks Joe Bob - WHACK.
Simple solution. If an ability's too broken, let the antagonists learn it, too.
~M.