This probably means nothing, but I find it interesting to consider.
Haman is throwing lots to select a date for the destruction of the Jews. He figures the lottery will fall out on a time that is naturally bad for the Jews. It falls out on the 12 month, the month of Adar. Haman is happy, we are told in the midrash, because he realized that in the month of Adar we find the death of Moshe Rabbeinu on the 7th of Adar. That obviously means the month of Adar is bad luck for the Jews.
As a side point, the gemara tells us that he did not realize that Moshe was also born in Adar, so the month of Adar is good for the Jews.
The passuk in the megilla just tells us that it fell out on the 12th month which is Adar. I find it interesting that the passuk that this is written in is passuk 7 (chapter 3). In passuk 7 we have the lots falling out on Adar, and Haman is thinking about the 7th of Adar.