A study of people with locked-in syndrome suggests not; the vast majority of those surveyed reported being happy.
If a terminal condition that permanently keeps you from moving anything but your eyes can’t make you unhappy, I doubt we’re measuring anything of importance. What if we do believe these measurements are accurate reflections of happiness? Then things are more problematic: this is a worst-case scenario of the Hedonic Treadmill, and happiness isn’t the measure of well-being we should be targeting.
To put it bluntly, if people are just as happy after developing locked-in syndrome as they were without it, should we stop treating or trying to prevent it?