No, not like that. According to Wikipedia:

Traditionally, the term referred to vehicles built on passenger car chassis and with the cargo tray integrated with the passenger body (coupé utility vehicles). However, present-day usage of the term “ute” in Australia and New Zealand has expanded to include any vehicle with an open cargo area at the rear, which would be called a pickup truck in other countries.

If you search for “cybertruck ute” you’ll find many publications from Australia and New Zealand calling it that, but I’m talking about the narrower first definition. It’s hard to say whether or not the Cybertruck chassis is a “passenger car” chassis because it is unique, but the cargo tray of the Cybertruck is definitely integrated with the passenger body. (Pickup trucks according to the American definition have a hap in the body between the cabin and the truck bed, and the Cybertruck does not.) So the Cybertruck definitely at least looks like a ute defined in the narrow sense.