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I'd say it can be written this way. Not that it is taught to be written so, or even encouraged, but everyone who reads it will understand what is meant. I do not believe this is a remnant from the Kurrent or Sütterlin, because there a bowed line denoted something completely different, as has already been pointed out.Two short vertical lines or even a wavy line denoted the Umlaut. Also these older scripts are not intelligeble to most younger persons, even in German speaking areas. Instead this is a very common way of writing these diacritic signs in other languages using these. In Swedish we were taught to write the dots as a curved line in cursive. https://sv.wikipedia.org/wiki/Skrivstil#/media/File:Svssfb.jpg (Nowadays cursive handwiting isn't even taught anymore.) The same goes for Danish and Norwegian. I therefore think it might have more to do with a common trait than with a supposed link to older ways of writing. The fact that writing this way in German could cause a confusion, because of the old n/u distinction function, should make it less approprate though.