Great question dreames and yes, this can be done. In order for the phone to be recognized as a Mass Storage Device you will need to make sure the phone as an SD card in it. If you check out the link below it will give you steps on how to get the computer to recognize the phone's SD card. The computer probably won't be able to access the phone's files that are saved on the internal memory without the assistance of the bridge. To get those files without the bridge, you'd need to transfer them from the phone's memory to the SD card, then from the SD card to the computer. That link has steps to do this also.
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