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No, you may cause damage to either PC, the USB/Firewire hard drive controller(s) or the drive.
Then again it might not cause any damage but it sure wont work how you want.
If you want simultaneous(ish) access, get a NAS enclosure for the drive.
Or mount the external drive as a network share on one PC and allow the other access.
Assuming Windows, right-click the drive and pick Share from the menu. The rest should be obvious if you have basic reading comprehension. Then the drive will show in Network on any other Windows machine on your network.