To be pedantic, this is not necessarily so, but most likely is the case, it just depends on how the IMAP client is set up.
With that being said, most IMAP users like myself, leave copies of messages on both the server and each device which accesses them.
This is kind of a poor man's backup, which in my case literally saved me a lot of time recovering my messages when my Solaris server had a hardware failure.
The FBI/DOJ has always had access to all of the emails, and was simply not interested in doing a serious investigation. Had they been, a Grand Jury would have been impaneled to investigate this issue 14 or 15 months ago. The fact that DOJ never permitted a GJ was the Big Tell, but there are so many procedural irregularities in the original "investigation" that it's pointless to claim that a particular mail protocol is now a game changer.
What changed here is that agencies outside of the Clinton Cartel have seen the emails, forcing the FBI to at least pretend to take a second look. My guess is they will try to destroy all of these records as well.