Yes you can, and it's very easy, here you go:
1. Disconnect the AC adapter.
2. Remove the bottom cover.
3. Remove the battery and hold the power button down for 10 seconds to drain all the power from the system.
4. Locate the HDD and remove the screws:
5. Use the tab to pull the HDD out of the system.
6. If you want to remove the HDD from the bracket, remove the 4 screws and pull it out.
Dell | Alienware Technical Support
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Thanks! Removed and reinstalled drive (didn't bother taking it out of bracket once removed) and it booted up without incident or error message. A bit mysterious as to why this worked...the way the drive is installed and screwed into the frame and connectors seems rock solid, but I'm not complaining. Thanks again!