I know that that variance of the difference of two correlated variables, $Y_1$ and $Y_2$ , is what the below formula shows, requiring $r$ the correlation between the two variables.

But suppose I have an amply large random sample of each variables, $Y_1*$ and $Y_2*$ in isolation.

Does variance of $Y_2* - Y_1*$ give me a good estimate of variance of the difference between $Y_1$ and $Y_2$?