Yes, you're right. The curvature, however, will be only half as big since the first half of the curving path from another star isn't there.
There is, however, another effect. Maybe by the "real" size you mean the distance across the sun, as measured by some local ruler. (Ok, let's not worry too much about the practicality.) That distance is
bigger than you would think from the apparent area or circumference, because of the way gravity warps spacetime
inside the sun. This effect on the apparent size is less than from the light curvature by a factor of about R/L, where R is the sun's radius and L is the distance from us to the sun. So it's pretty small compared to the light curvature effect.
Mike W.
(published on 02/21/2013)
