I am changing webhosts and will be using the new hosts mail servers instead of the old ones.

I have created all the correctly named mailboxes on the new service but have also not yet cut ties with the old webhost. I am expecting that even if the new DNS values which point to the new hosts DNS servers and respective SOA\zone file with the new MX values have not yet propagated and an E-mail is directed at the old hosts mail servers as per the mx records in the SOA\zone records which the old hosting provider holds, the E-mail would still come through to the mailbox that's on the old host providers mail servers. So I am just trying to reaffirm if I got this right and it's essentially impossible for me to loose an E-mail since it will hit either the old hosts mail servers or the new ones ?

Also is it possible to configure the same E-mail account to check and collect mail from different mail servers by entering multiple pop3 addresses ? And if I choose to keep the old web hosts mail hosting services as a backup by specifying the mx records for it with a lower priority in the SOA records hosted by the new webhost, is it possible to have any incoming E-mails sent to both servers by the mail daemon so I have two copies? Or is my only option having the primary mail server forward the E-mail somehow to the old mailserver ?