Is sugar necessary for the texture of homemade sherbet?
That sounds to me like it'd come out completely rock hard once fully frozen. Immediately after churning while it's still just barely frozen it'll probably be okay, but I'm not sure if it'd make it through six hours in the freezer.

You have no fat to soften it (the thickeners in fat-free half-and-half doesn't really do much), and essentially no sugar (just the bit from the orange juice), so there's nothing to stop it from just freezing.

Homemade ice cream/sherbert/sorbet tends to come out harder than storebought things to begin with, thanks to the lack of softening additives and often people being a bit more conservative with fat and sugar. For example, frozen yogurt with full-fat yogurt and a decent amount of sugar can still end up solid and unscoopable once frozen, and the same can happen with more lightly sweetened sorbet unless you add alcohol. Taking the fat and sugar all the way out without compensating doesn't sound feasible.