The CSR at Tuft Paw could not tell me whether the litter will work in a Litter-Robot by Whisker (which our cat loves, BTW). So I am contemplating continuing to use our commercial cat litter in there but changing out to the natural cat litter in Kitty's second litter box in my home office. Can we expect success routinely using two different kinds of litter?
If I have understood your question correctly, you're wondering if it is ok to use a different litter type in each tray?
Yes, for most cats this won't cause an issue.
The exception would be very sensitive or fussy cats, who may find this stressful or who may dislike a certain litter type. So, it is worth just keeping an eye on both cats to ensure they continue to use their trays as normal and develop no new signs (such as peeing outside of the box).