sort of, using Trace Reference - but the dimensions and other annotation will not automatically adjust for the rotation and would need to be on a different layer if they need to stay oriented with alternate building rotation.
Something like this could work if just rotating the layout is not sufficient.
I agree, it's confusing and not intuitive. I think it is an unintended consequence of combining rotation and zoom, and possibly a bug.
After I checked the "ignore zoom" checkbox in the view settings, my saved rotated view was still correctly rotated (rotation was not ignored) on the layout, but no longer rotated when I went to the saved view. View settings does not tell me that this is a rotated view. Neither do the drawing selection settings for the layout, which explicitly tells me the drawing is not rotated even though the view, as shown on the layout sheet, is correctly rotated. If someone else needed to open my model to use it they would be totally mystified.