I would not call it a correlation. You have to consider genetics. A leghorn will be smaller yet lay a fairly large egg compared to most dual purpose hens. Hens from the same breed can lay different sized eggs and have a fair difference in body size, especially those from hatcheries. I often fine that the smaller hens of the same breed lay larger eggs.
Chicks that hatch from the small pullet eggs are going to start out smaller and have trouble catching up in size to chicks that hatch from larger eggs. I agree with that part. But I think there are too many other variables to say there is a correlation.
Something I’ve noticed from hatching pullet eggs. I normally get worse hatch rates with those tiny pullet eggs. It’s not that I get lousy hatch rates, just that if I have the same number of little pullet eggs and regular eggs in the incubator more of the ones that don’t hatch are the little pullet eggs.
I hardly ever lose any chick that I hatch, whether in an incubator/brooder or with a broody doing all the work. But when I do lose one it is practically always the ones from those tiny pullet eggs. They are just smaller, weaker, and more delicate; harder to raise. If they get past that first week they usually do great. But that first week can be tough. I’m not saying that most of them die. I’m saying if one does die, it probably came from a little pullet egg.