Move to Online Mode only one site of two multi sites sharing the same code base
if you mean "update" with "put online" then it is not possible, because - as you pointed out - all sites share the same code base.. updating the sites/all folder will update both. the database updates need to be performed separately.

if you have only one website online that you want to update then just upload the changes from the sites/all folder.. that updates themes and modules.

cheers,
j