The SMTP plugin doesn’t seem to like it when you put a Gmail address in the From field… or maybe Gmail doesn’t like being used in WordPress. Hmm…
Anyway, I created an email address using one of my many Godaddy email hosting credits, forwarded the email to my Gmail, and put that email in the From field. Worked fine (test returned "true" instead of "false").
Be sure to read Part 1 here.
Update 2009-08-28: While Gmail addresses do not seem to work in the From field, Google Apps email address do!