Hi Jeremy,
No, observational evidence does not support that hypothesis. If it were true then there would be a 'center of the universe' but when we look out we see uniformity in all directions including the 'expansion rate'. As far as we can tell we are the center of the universe. An observer on Alpha Centauri would come to a similar conclusion.
You might type in 'expanding universe' into the search box to find some more discussion on this topic.
LeeH
Here's some older answers that discuss a problem that would come up with any picture of a single huge star expanding- it would collapse into a black hole. /mw
(published on 10/25/2014)