I don't know much about prospecting in New Mexico, but in Colorado, you usually need permits for gasoline (or diesel) powered water pumps, but not for electric powered bilge pumps (altho there are some places that don't allow any motorized gear, such as Cache Creek near Leadville). Gold Cubes don't work well with too much water flow - the electric bilge pumps are what you will be using with one anyway. I would suspect that the bilge pump is not going to be an issue. So, as long as the site allows a sluice, it should allow a Gold Cube.
You need to look at your state recreational mining regulations to see what restrictions you have. You might consider attending a few meetings at a gold prospecting club (if you have one near you) - odds are good that someone in the club knows what the restrictions/limitations are for where you want to go.
There is a GPAA club in Roswell NM - look them up (It's free to attend GPAA meetings and you don't have to join the GPAA to go to them).
I bought my Gold Cube over a year ago, and I don't use my old sluicing gear anymore.