Gmail – Using Gmail for several e-mail accounts with IMAP

You're going to have to work around this a little bit yourself. What you will need is a daemon or frequently run job that fires off something like fetchmail which is configured to login to your imap account, suck off your mail and either forward it to your gmail address or manually deliver it into another imap account (again, your gmail box).

This will need to run from somewhere consistently in order for you to have your mail up to date, but it doesn't have to be the box you check your mail from. You will be able to use your gmail from anywhere as usual as long as that fetchmail or similar is running somewhere acting as that little tunnel porting mail from one place to the other.

A message is considered recent when it has the \RECENT flag:

From the rfc3501

   \Recent
       Message is "recently" arrived in this mailbox.  This session
       is the first session to have been notified about this
       message; if the session is read-write, subsequent sessions
       will not see \Recent set for this message.  This flag can not
       be altered by the client.
       If it is not possible to determine whether or not this
       session is the first session to be notified about a message,
       then that message SHOULD be considered recent.
       If multiple connections have the same mailbox selected
       simultaneously, it is undefined which of these connections
       will see newly-arrived messages with \Recent set and which
       will see it without \Recent set.

So, as long as the client checks the recent flag you should blame IMAP...