Assume, we have the following:
$U$- unobserved confounder
$V$- instrumental variable.
Assume there are no observed confounders.
Can we check the assumption of exclusion restriction by running a regression of $Y$ on $D$ and $V$ and testing if the coefficient associated with $V$ is 0? The rational is all the effects of $V$ on $Y$ has to go through $D$ so once $D$ is controlled, there should be no effect of $V$.