An SMTP session between two mail servers may be encrypted, but only if both ends support it and if both ends choose to use it. So if you're sending mail from Gmail to example.net, then Google could only encrypt if example.net was ready and willing. For this reason, you cannot trust email to be even moderately secure at the transport layer. (The only safe end-to-end method is to encrypt your email using S/MIME or PGP, but the people you're exchanging email with need to be on board too... just like the mail servers).
As to whether the big three are performing opportunistic STARTTLS, I haven't seen any evidence of it, but I spend less time reading my mail server logs than I used to. And if they are, they're still only half of every SMTP connection they make, and cannot guarantee the use of encryption.