Do SD cards operating at 1.8V save any power compared to 2.7 - 3.6V?
I think the introduction of 1.8V was mainly to get higher frequencies and more speed on the data lines. If I read the specification correctly, VDD isn't actually reduced to 1.8V. Only UHS2 have a separate VDD2 at 1.8V. So probably the only benefit you get is higher speeds and a slightly lower current consumption because the I/O lines have less voltage swing, but if you need level shifters there won't be a benefit (on the contrary). 

3.3V lines are specified up to 50MHz. Whereas 1.8V data lines can go up to 208MHz.

I might be entirely wrong though, SD cards take way too much power to be used in my projects, so haven't worked with them in detail.