No, we do not allow any excavation for the covering of footings and bases for sculptures. (Our agreement with the Bureau of Land Management only allows us to dig holes up to 12"x12" and 3' in depth.) Some artists build platforms to cover their base. Others buy or rent steel trench plates, lay them on the surface of the playa, and attach their artwork to that. You can use accumulated playa dust to cover plates, but you cannot trench or excavate to cover them.
You can also use guy wires attached to ground anchors. The type of anchors we can provide, install, and remove for you are 48" long with an eyehook at the top. They have an observed failure point of 3,000 lb. each (in vertical tension, 90 degrees to the ground). You will need to bring your own rigging/turnbuckles to tie down to the anchors. See images here.