Yep, I'd dig seeing it. Technically they are prohibited from "running" for the position. Of course, it is just chance that some of em decide to visit a bunch of the lodges known to have a regular and sizable voting presence at GL every year. Wink/nod.
As long as you maintain that little nicety in your tone and approach I don't think GL will have anything to say about it. Just approach the dudes directly, no need that I can see to let the PGMs put their thumb on the scale and make ya feel like you need to go hat in hand, and through them. Their power derives mostly from what you grant them.