Well I have a few mechanical watches (automatic and manual winding ones) and since I do not wear them all at the same time they do run out of power rather often. If anything, make sure you wind them about once a month to make sure the gears don't get gummed up as you say but otherwise it should be fine.
This is my opinion but I've never had an accuracy problem due to the fact that I wasn't wearing them. 
EDIT: Really, where are my manners!? Welcome to TRF!
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Mon corps c'est un pays en guerre sur l'point d'finir,
Le général de l'armée de terre s'attend au pire,
J'ai faim, j'ai frette, je suis trop faible pour me lever debout,
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- André Fortin
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