# Newey-West standard errors with cross-sectional OLS?

Consider the cross sectional:

$Y_i = a + b X_i + e_i$

where I have reason to believe that $E[e_j e_k] \not= 0$ for a concerning number of $j\not= k$.

What happens if I use a serial correlation robust standard error here (such as Newey West)? Is it okay to do so even though, of course, I have no serial correlation in my data, yet I have dependence? Will Newey West correct for the fact that I have non-zero non-diagonal elements of my variance-covariance matrix?