If your code is able to access that folder, then yes.
Perhaps you're accustomed to your mail client automatically putting a copy of all sent messages into a folder named something like "Sent Items"? Then yes, you can do that too. You just have to write the code which puts the message into an (IMAP) folder after you send it (via SMTP).
That's not your job, that's the job of the mail server. You send the message to the mail server using SMTP,
the mail server puts the message in the recipient's Inbox. Possibly the mail server supports some sorting
or filtering options that allow the recipient to control exactly what happens to incoming messages.
As the user of an e-mail account, I'm the one who should decide what happens to mail which arrives at my account. If I want to put it into a folder, I will do that. If I want to delete it without reading it, I will do that too. It is absolutely not all right that anybody sending me e-mail can do anything with my e-mail account except send messages to it.