Is it possible to make outgoing mails sent via the SMTP server appear in my sent folder in Zimbra?

Yes it is possible, subject to support from your email client software. 
If you are using Zimbra Desktop or the Zimbra Connector for Outlook or Zimbra Mobile on an iPhone or Windows Mobile device – sent items are automatically copied to your sent folder on the server. You will not need to do any special configuration. 
Generally speaking, if you are using POP3 (not recommended) it is not usually possible to copy sent items to the server. 
Again, generally speaking, if you are using IMAP in most modern email client software, you may be able to configure it to copy sent items to the server.

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