Applying Ripple to a DC Source?
Q: Can I put a large inductance between the battery and the capacitor such that none (or very little) of the AC voltage is seen at the battery?

A: Yes, that is the way to go

Q: Does the function generator need to be able to source much current?

A: that depends on the AC input impedance of your equipment under test. (You can test it: The function generator will not get damaged)