The power is negligible. It won’t affect your power bill in any noticeable way. I know because mine are all on backup power supplies.
The complexity / double NAT concerns are also inconsequential. I was concerned but it works great and quickly.
Discussion
Something like $40 per year in power bill, maybe
I guess that depends on your rate. My napkin math puts mine at about $25 per year based on my local power rates.
I also basically have baseload covered with my solar too, so mine is closer to “free” in the sense that I will produce more in net metering credits with the power company than I will use and adding a few more watts won’t make it go negative either so I can use it.