Is it true that non-profits can run free AdWords campaigns?

You're making a common mistake in your question that I have to correct before we go any further: AdSense is the network of advertising, the "publish" side of the equation, and it's aimed at bloggers like me and other sites where Google can display relevant adverts and share the revenue with the individual publisher. AdWords is the advertiser side, and an AdWords campaign encompasses both a mechanism for injecting ads into the AdSense stream and ads onto Google's search results and related pages. You're talking about AdWords since you want to advertise.

Now, yes, your friend is correct and though little known, Google has a generous program called Google Grants. As the company explains:

"The Google Grants program supports organizations sharing our philosophy of community service to help the world in areas such as science and technology, education, global public health, the environment, youth advocacy, and the arts... Designed for 501(c)(3) non-profit organizations, Google Grants is a unique in-kind advertising program. It harnesses the power of our flagship advertising product, Google AdWords, to non-profits seeking to inform and engage their constituents online... Google Grant recipients use their award of free AdWords advertising on Google.com to raise awareness and increase traffic. "

• Google Grants Quick Tour
• Details of the Google Grant Program
• Frequently Asked Questions about Google Grants

The upshot of this is that if you're focused on helping women out, you'd probably be eligible for a Google Grant and be able to gain some advertising reach without cost. Certainly it'd be useful to match searches like "women's shelter XX" where "XX" is your town or city name. If you delve into lobbying on behalf of women, or abused women, or similar, then you might have a problem and it might be smart to spin that lobbying effort off into a related, but separate LLC or organization.

Having said that, I don't know of any non-profits that have received a Google Grant of this nature, so I would love to hear from anyone whose organization is enjoying this largesse from Google. Certainly it's a splendid idea, and the fact that one of my favorite organizations, UNICEF, is listed as a case study for Google Grants is way cool in my book.

Good luck to you. May we one day live in a world where we don't need women's shelters, but in the meantime, keep up the good - and important - work.