I would be thankful if someone could verify the following reasoning.
Let $I$ be some graph property that is invariant (chromatic number, connectedness,etc.). Let $p(n)$ be the number of (labeled) graphs of degree $n$ that have property $I$. Suppose we know that almost all graphs have property $I$ that is to say
$\lim_{n \to \infty} \frac{p(n)}{2^{ {n \choose 2}}} = 1. \; \; (1)$
Does it imply that almost all non labeled graphs of $n$ have property $I$ as well?
My reasoning would say YES, since the number of all non labeled graphs is asympototic to $\frac{2^{n \choose 2}}{n!}$ and the size of the automorphism class of almost all graphs is $n!$ so if $p'(n)$ denotes the number of non labeled graphs we would have $p'(n) \sim p(n)$ and using a simmilar limit as in $(1)$ one derives at the conclusion that the given property also holds for almost all non labeled graphs.
Is the above true? If yes then this would be (in my opinion) quite nice since one can derive such results for labled graphs (which is in a way easier) and have the non labeled result "for free".