I’m a wee bit skeptical, for a few reasons. Firstly there’s the reductio ad absurdum problem: if handwriting is good, then quill pens are better and pressing the tip of a quill into soft clay is better yet.
Then there’s the issue of actual learning: the method of information capture matters far less than the ability to discern what is important and what is not. This is a matter of pedagogy, not a matter of technology per se.
After this comes the matter of volume — we can type far, far faster than we can write. Provided we’re capturing the right information (see the point above) it makes far more sense to do so rapidly rather than slowly.
I could go on and on, but the key point is this: learning is about understanding, not primarily about memory. I may memorize a great many useless facts by writing them down but this does not imply understanding. Yes, we do need students to understand how calculus works rather than have them merely pressing buttons on calculators, but there is no necessary link to handwriting — there are plenty of ways to ensure students go through each step in turn and understand the fundamental concepts before using technology to speed up their calculations.