Well, they would of course have access to the content before it's encrypted. I don't trust someone else to perform the encryption for me, even on the client side, after everything that happened. But then, even your own OS, all the software that's on your machine, there are sooo many parties involved with so many affiliations, objectives, incentives. If it's not NSA that's peeking through your SSL connection, then it's probably China that bought off your antivirus manufacturer or a Russian hacker who injected something vile in an open source library that covers 90% of the internet connected world or someone we haven't even heard of who hardwired all keyboards straight from in the manufacturing plant to phone home your input. Hell, they could even be peeking through the window.
If they want to read it, they will. If you desperately want to avoid it, don't use Yahoo of GMail in the first place, not even with "encryption". I'm cynical enough to think this will not prevent them from reading your content, Yahoo will have a similar gain by accessing your content (why would they start the service in the first place) and they don't seem to mind.