First, the caveat: You can read data from a closed workbook, but you cannot write data to a closed workbook. Workbooks have to be opened for data to change. So if you don't mind that workbooks are automatically opened, processed, saved, and closed in sequence, there should be no problem to the operation. NOTE: the workbooks may be opened with no visibility so you won't see the applications flashing on and off. (NOTE: I am 99.9% sure one cannot write to a closed workbook, but there may be that 0.1% obscure super-duper API-level method that could make it do it; having said that, I doubt it could be done because if it could, some enterprising scriptwriter would most probably have made a wrapper for the function in the first place; none exists as far as I know.)
However you didn't indicate a sheet name, just cell ranges. I can make an assumption that all the target sheet names in every excel file is either named the same, or alternatively, is the first sheet in the tab sequence in each file. Otherwise you would have to do a laborious search process to indicate that the source cells are, indeed, of the data you are looking for in the fist place before processing.
I'm currently at work so not in a place where I can easily write a code snippet, but if you make use of the file system object (or more crudely, the DIR function), you should be able to achieve the above. There are several threads on VBA that open/close a workbook in this forum, start at those.