The volunteers who wrote by hand
learned unfamiliar letters more quickly, and did better on some related tasks after a small number of alphabet lessons: 'naming letters, writing letters, spelling words, and reading words'. It's not very surprising that physically forming a set of symbols will get their shapes into your head quicker than simply pressing the corresponding buttons. But that doesn't tell us much about any potential benefits beyond this very early, low-level learning.
Learning higher-level features of the language (and even growing your vocabulary, once you've got past the point where letter shapes are a stumbling block) could just as easily be slowed down by handwriting, for the same reasons that it apparently helps in the complete beginner phase -- it forces you to slow down and expend more effort on the low-level task of letter formation.