It's possible. iTunes 9.2.1 is the last version to run on Tiger, and it was last updated in 2010. The current generation iPod classic (7th) came out in late 2009, so it should be compatible. However, later software updates to the iPod may have made this untrue.
On Apple's site it specifies iTunes 10.7 or later, and OS X 10.6.8 Snow Leopard (Intel only).
Officially, no it won't work. But it might.
You could also pick up a 5th gen iPod video that would work with it. I bought a couple. One I put a CF Card in, the other, a 120GB HDD. For less than the cost of a new Classic that I also have. I have an iBook on Tiger and the current classic to test with, but the iBook's DC board is shot for the moment, and I can't locate the charger 🙄