I currently own a Motorola Droid 3 on Verizon.
I wish to purchase a LG Nexus 4 directly from Google - will it work on my Verizon Network? Or would it be a waste of time?
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It would be a wast of time (and money). The phone is not compatible with Verizon's network.
Verizon is a CDMA network, and the Nexus 4 from Google is GSM phone.
In the past Google has met-in-the-middle with Verizon and released the CDMA compatible Galaxy Nexus - this time there appear to be no plans on releasing a CDMA compatible Nexus 4 (possibly due to the slow turnaround time Verizon had on releasing updates to the Galaxy Nexus).