Do warnings verify better nearer radars?
This may/may not actually answer your question "Do warnings verify better" because of the qualitative word "better" and other factors that play a role, such as terrain and forecasting office. Another factor to consider is the nature of the warning and size of the phenomenon. A radar, for example, may not be the best tool to show verification of a hurricane, but it may be better for verification of a tornado. I hope to answer your question by taking arguments to the extreme.

If warnings verify more and more accurately as the warnings get closer to the radar, they may end up in the "cone of silence," where the angle of the radar would not be able to capture the phenomenon.

The opposite of that statement would be that warnings are more accurate the farther away the phenomenon is from the radar. This is also absurd, not only is resolution of the radar cut, but the curvature of the earth also makes this idea absurd.

Conclusion: there is some middle ground. If you get to close, you may not only be endangering your radar (depending on the phenomenon) but you may miss data. It also matters what angle your scan is at. I would hypothesize that anything within the highest elevation angle of the radar would have the highest accuracy, but it would really matter what the phenomenon warned is and what size the phenomenon is. 

Warning zones are issued by people, and people have flaws. I would hypothesize that your results may not be conclusive, since the habits of each WFO may vary. For example, a winter storm warning in Georgia is an inch of snow and ice, while Boston would need 6 inches of snow to issue a winter weather watch. Some areas see tornadoes more often than others, leading to some inherent biases, etc.