[Dovecot] Server-side sieve for client-side copies

I know I could test this - but I'd rather ask first. To my knowledge, we haven't come up with a good server-side implementation for savings copies of sent messages (by all means correct my ignorance in this regard). So the typical way is to enable it in clients like Thunderbird (this prompted a whole discussion of how to save these messages without sending them to the server multiple times).

My understanding is that sending a message from a client (use Thunderbird for simplicity of this conversation) is performed via SMTP.
Saving a copy into a sent folder is performed via IMAP (hence the multiple transfers to the server). Now that I've laid a background - let's make it Dovecot specific. I don't know how "behind-the-scenes" Dovecot performs the act of saving mail messages that it receives from IMAP, instead of SMTP. Specifically, if I'm using sieve filters via deliver - can I setup a filter that will place mail copies to specific recipients into specific subfolders?

Daniel