No way. Sheldon claims that a circular or elliptical ring will engage the same number of teeth. But even if this is true, the angle of the chain coming off the top and bottom of the ring will be different. Therefore creating a different distance to the cog. Therefore more chain required sometimes than others. Therefore different tension through the rotation.
But, the real question is whether or not there is enough difference to matter.
All I know is that if I have my chain at max tension when the ring is at one point in its rotation, I can still slip it off by hand when it is at another.