Gotta love static electricity. I did try finishing the contact to see if the aerogel was an insulator and heard a fizzling noise, as though it contacted a bit. So I figured we needed a better test...
The scale to measure by is the green one on the top. Now let's try the aerogel:
As you can see, the resistance of the aerogel met infinity. Realistically speaking there probably is an upper limit I just don't have the means of measuring it. It's important to understand though that while it is an electric insulator, it's a pain to work with due to that static electricity and I'd be worried about arcs with higher voltages. Be careful!
Credits
Thanks go to my fiancée Shuana for jumping in head first with aerogel... for two years! I love you cutie!