Forgot to answer the other bits:
Subs will generally still work  as long as there's no selection going
on (which there sometimes seems to be in some copy/paste operations,
though not explicitly). A few other commands also need the sheet  to be
visible, but try it and see. If the code falls over, you can
temporarily make the sheet visible again
(Application.ScreenUpdating=False) while that code runs and make it
invisible after the code has run. The brief screen changes associated
with this can be hidden from the user  with
Application.ScreenUpdating=False before unhiding and rehiding, and
Application.ScreenUpdating=True afterwards.

I think calculated values on other sheets  will be OK as long as you
haven't switched to manual recalculation. But try it!