I had a brief look at the literature and found a few reasonably relevant papers.
First, individual letters are more accurately recognised when written than when typed:
Recent data support the idea that movements play a crucial role in
letter representation and suggest that handwriting knowledge
contributes to visual recognition of letters. If so, using different
motor activities while subjects are learning to write should affect
their subsequent recognition performances. In order to test this
hypothesis, we trained adult participants to write new characters
either by copying them or by typing them on a keyboard. After three
weeks of training we ran a series of tests requiring visual processing
of the characters’ orientation. Tests were ran immediately, one week
after, and three weeks after the end of the training period. Results
showed that when the characters had been learned by typing, they were
more frequently confused with their mirror images than when they had
been written by hand. This handwriting advantage did not appear
immediately, but mostly three weeks after the end of the training. Our
results therefore suggest that the stability of the characters’
representation in memory depends on the nature of the motor activity
produced during learning. (Longcamp et al., 2006)
A subsequent fMRI study found that when people were required to recognise letters they had learned before, participants' brains were more active in areas associated with execution and observation of actions, suggesting that you're right, it seems the movement associated with handwriting does help with recognition.
Secondly, and more directly relevant, children's spelling is better when words are written when learning them, than when words are typed:
Previous research has demonstrated the superiority of a Simultaneous
Oral Spelling method for young children beginning to learn to spell
words. In this technique, children learn words by repeating a word
spoken and written for them, writing the word while pronouncing the
name of each letter, and then repeating the whole word again. In two
experiments, we manipulated the motoric element of this training and
obtained results indicating that having first-grade children write
words leads to better spelling performance than having the children
type them on a computer or manipulate letter tiles to spell them. The
superiority of handwriting was maintained even under conditions where
post-training spelling assessment was done on the computer and with
tiles. (Cunningham and Stanovich, 1990)
It seems rather unlikely that the handwriting advantage would exist at the letter and word levels, but end there, so I strongly suspect text would be better remembered when written by hand compared to when typed.
