No it will not. Incidence matrix is a matrix where rows represents vertices and columns edge numbers. We dont know the label of edge between $i$ and $j$ beforehand. So to check whether an edge exists between $i$ and $j$ , we will check each column in worst case to check whether both $i^{th}$ and $j^{th}$ contain 1 in the same column. So worst case complexity will be $O(E)$ in case of incidence matrix.