I feel terrible about having mispoken on this, so I ran a quick test just to be completely sure. As it happens I have both Gomadic's battery pack and a Tekkeon pack that also takes 4 AA batteries.
I used the same batteries in both packs, and the same iPod cable, so the only variation is the battery pack itself.
The Tekkeon was able to trigger the iPod touch charge circuit using 4 rechargeable batteries AND 4 new alkalines AND 4 new non-rechargeable lithium AAs.
The Gomadic was able to trigger the charge circuit using 4 rechargeables but NOT with the new alkalines or lithiums.
So if you use rechargeables, either is fine.
Sorry for the confusion, I guess I need to drink more coffee. Or something.