Mental rotation as, probably, any mental movement or transformation of objects, obviously involve motor areas of the brain
(see e.g. Pellizzer G. Mental transformations in the motor cortex. Brain Res Cogn Brain Res. 1996 Dec;5(1-2):123-30. ;
Sasaoka T., Mizuhara H., Inui T. Dynamic parieto-premotor network for mental image transformation revealed by simultaneous EEG and fMRI measurement. J Cogn Neurosci. 2014 Feb;26(2):232-46. doi: 10.1162/jocn_a_00493.)
There are several studies, showing relation between mental rotation abilities and motor learning and skills in infants, as well as in older children
(for example, Möhring W, Frick A. Touching up mental rotation: effects of manual experience on 6-month-old infants' mental object rotation. Child Dev. 2013 Sep-Oct;84(5):1554-65. doi: 10.1111/cdev.12065. ;
Frick A, Möhring W. Mental object rotation and motor development in 8- and 10-month-old infants. J Exp Child Psychol. 2013 Aug;115(4):708-20. doi: 10.1016/j.jecp.2013.04.001. ;
Schwarzer G, Freitag C, Schum N. How Crawling and Manual Object Exploration are Related to the Mental Rotation Abilities of 9-Month-Old Infants. Front Psychol. 2013 Mar 4;4:97. doi: 10.3389/fpsyg.2013.00097. ;
Jansen P., Heil M. The relation between motor development and mental rotation ability in 5-to 6-year-old children. International Journal of Developmental Science, 2010; 4(1): 67-75. ;
Wiedenbauer G., Jansen-Osmann P. Manual training of mental rotation in children. Learning and instruction, 2008; 18(1): 30-41.).
There are also publications, demonstrating or proposing the role of movement imagery in motor learning
(Ryan E.D., Simons J. Cognitive demand, imagery, and frequency of mental rehearsal as factors influencing acquisition of motor skills. Journal of Sport Psychology, 1981; 3(1): 35-45. ;
Jackson P.L., Lafleur M.F., Malouin F., Richards C., Doyon J. Potential role of mental practice using motor imagery in neurologic rehabilitation. Archives of physical medicine and rehabilitation, 2001; 82(8): 1133-1141. ;
Dickstein R., Deutsch J.E. Motor imagery in physical therapist practice. Physical therapy, 2007; 87(7): 942-953.).
I don't know papers, showing that practice in mental rotation improves corresponding motor skills. But concerning the evidence above, I suggest that such effect should be highly probable. The question is rather in choosing the relevant forms of practice tasks and motor skills tests.
Hope I understand your question correctly and my answer will help you.