Looking at the other, much clearer image from the article about the founding of the Blind School (shown below) I don't think the front on London Road was remodelled to become the post 1851 version. The image below shows that the central portion of the old building projected forward slightly from the two single storey wings. They probably took it down to the foundations of the original building so that the new building had a similar footprint, and may have reused some of the architectural stonework, but other than that I think the current building completely dates from the second half of the nineteenth century.
Based on the 1871 census when there are 14 people living at number 32, I think the premises must have extended out to the rear, along Hotham Street, some distance as shown on the town plan for there to have been space for warehouse storage there as well. I doubt very much that the bricked up window had anything to do with the window tax. It could be a much more modern alteration, perhaps following the remodelling in the late 1940s/early 1950s when the cinema was built next door.