Yes, but it's between your MUA and your server. S/MIME, as far as I know, does not do server-to-sender public key exchange. If I send a signed message to you, then you have my public key and can encrypt messages to me, yes, but you can't get my public key from the server.
Frankly, S/MIME is really the best solution available today. It works with gmail (not web-mail but using a MUA). Most MUAs support it. It's easy to get a free personal S/MIME keypair from a CA. Google, Apple or whoever you use for mail never sees your private key and can't read your messages.