Stop gradient operation prevents the gradients to be calculated for the proceeding graph. However, skip connection outputs are added to the sub-network being skipped over.
The question is about placing a stop gradient ($sg$) operation on the identity path, $x$, of a residual block $r(x)$, that is: $r(x) = sg(x) + f(x)$, where $f(x)$ usually represents a couple of convolutions with batch-norm.
In general the stop gradient operation tells auto-diff to treat that expression as a constant, so when asking for the derivative of $sg(x)$ it should be the same as differentiating a constant value.
In practice, I think that $x$ or, $sg(x)$ (since it returns $x$ but without tracking its gradients), still accounts for the forward pass of your network but not in the backward pass since backprop would only consider $f(x)$ and not also $x$.