Gmail de-duplicates emails. When you send a mail, the copy which comes back in is found to match the copy you already have and ignored. This is why mail you send from your own address often just appears in Sent Mail.
Sent Mail is still in the conversation, and should still have the References: headers to allow it to be threaded.
I suspect that you're using Gmail filters to tag mails based on the list as they come in? So this works in Gmail because when you look at a label in Gmail, you select conversations (threads) rather than messages, so you get all the replies. The mail you sent won't itself have the label though, so on a strictly message-based interface such as IMAP that mail won't appear in the folder.
If you're using listid: to filter mail in Gmail, try using list: instead. The list: operator handles the To: header, as well as List-Id:, so is better than the listid: operator (which is just too low-level). Use <...> around the list-id to change the tokenisation to be more appropriate (and the '@' is a magic @ here, which will match the '.' form in the List-Id: header).