Not at all. It woul be trivial for them to steal your private keys from their web client. And yes, we have the code. But it's impossible to verify that the code that is on Github and the one they send to your browser every time you log in is exactly the same.
Also, they make it quite hard to make an anonymous registration. And they've been cooperating with governments. Don't get me wrong, I don't support criminal activity. But I don't trust any government with citizen's data, Snowden proved that.
Edit: Oh and they have bribed various privacy related sites with their affiliate program to recommend their services, which I consider a shady tactic.