My cursive education was rather flawed, and I curse it! For me, cursive was taught to be about proper letter formation, with no emphasis on the claimed practical benefits of writing faster by not lifting the pen. We did, however, learn “cursive” numbers. I don’t know that there was any implication that they should be written without lifting the pen. But they were considered to be the properly formed numbers to use when including numbers in a document you were writing in cursive. For example, the 2s had loops, not straight lines at the bottom.
I’ve had classes where taking notes involved rather a large amount of numbers. But legibility trumped speed by quite a bit in terms of what was important there, so I don’t think I would have chosen to connect numbers using cursive even if it were possible.