Can All-on-4 upper work with a crossbite? I do have some gingivitis.

Years ago I was told I needed braces &jaw surgery to correct my bite. Upper is not perfectly shaped like a horseshoe, rather one side goes flat just left of center where it should be rounded out horseshoe style. The cost stopped me before, jaw surgery was not covered by insurance, now 10 year later I can do the braces and jaw surgery but am advised to do upper all on 4.