Hi Mike,
I believe so. Should just be a matter of deleting the joints. I think the biggest issue might be trying to remove the finger geometry and filling the hole... Maya doesn't tend to like the geometry being modified after rigging.
one way to avoiding this, is by making some extra joints, we could e.g. call them bindjoints, which are parented to each joint that needs it...
example...
LeftHip_BindJoint parented to LeftHip...
LeftKnee_BindJoint parented to LeftKnee... etc.
then Bind the geometry to these Bindjoints, and if you e.g. need to make changes on the skeleton, you unparent the Bindjoints from the skeleton... and when you are finish with modifying the skeleton, you parent the Bindjoints back to their respective skeletonjoint... 
regards
Strarup
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Alex V. U. Strarup
One mistake can ruin it all...