Sure, it could make sense, just like the v-measure. Whether it is useful to treat the rows (or columns) as a regular clustering solution depends on the biclustering algorithm and the dataset.

For instance, the silhouette score might make more sense for the Spectral Biclustering algorithm, especially after normalizing the data, than it would for Spectral-Coclustering, because the rows of a checkerboard structure should be similar.