Having a reference call potential employer?

I will be graduating college in 2 weeks and am applying for jobs. One job I'm really excited about didn't ask for references for the application. A professor, who I have been listing as a reference for other positions, offered to call employers to put a good word in for me. The position in question is for a Community Organizer for a political action committee with a liberal bent.

Would this be beneficial, or would it have a negative impact on my chances? As far as I know, this reference doesn't have any personal ties to the organization.

Edit: Also - the PAC has a sister organization (same name, same website, same building & office, slightly different approach to achieving the same mission. One is a 501(c)(4) and the other is 501(c)(3) status for legal/political reasons). A woman on the board of the sister branch came to my campus to speak a few weeks ago, and I talked to her personally and bought her book. Should I send this woman an email? She's not on the board of what I'm applying for - she's in the other branch.