I would be more inclined to believe that your vibration is related to a bad/worn engine mount(s) than the water pump. Another possibility is that the coolant dripping on the oil level sensor may be causing the computer to mis-adjust the engine causing it to vibrate.

You can easily rule out the water pump when you replace it.

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Ray
1998 Mercedes E320, 200K Miles
2001 Acura 3.2TL, 178K Miles
1992 Chevy Astro, 205K Miles