I would never give access to my email account to a fly-by-night SAAS service. Nevermind the privacy concerns of mining my data, I just wouldnt trust their security practices unless they prove otherwise. An email nowadays is considered your identity. Any breaches to it can have a number of social, professional and financial implications.
Case in point, unroll.me mentioned in this article has a number of issues [1] [2] and response of Josh Rosenwald, founder of unroll.me at [3] dismisses that risk for perceived convenience.