Do blogs really work to keep people informed of your ministry? If so, what's the best way?

Yes! 

Blogs allow your readers to comment and interact with you. It's let formal than a website and your readers can stay informed of the updates via RSS feed (http://www.whatisrss.com).

Update often; let your followers hear personal stories about what is going in your ministry. Keep the postings shorter and add pictures to create a deeper level of connection with your readers. 

Keep your blog simple, clean, and easy to read. Don't overpower your readers with too many graphics and a distracting background. 

Should I ever strongly suggest support raisers to use or not use social media?

I would never strongly suggest that support raisers use Social Media. 

Social Media isn't a miracle cure. It might take sometime before a person's Social Media investment pays off... it might never pay off.  It's not a "one size fits all"; do what is right for you. Keep trying different methods.

It's just one tool: Don't over-invest. Don't neglect conventional media--you might leave our core supporters. Don't under-invest either.