The e-mail client is far behind that of web based e-mail clients such as Horde and Roundcube.
I imaging it would be terribly difficult to catch SuiteCRM up to that level of functionality (but wow if you could!). Therefore, my suggestion is to add “Sync Changes” to personal e-mail accounts. Users could then user their webmail client of choice–avoiding the costly IMAP back-and-forth on personal accounts–and INBOX, SENT, etc., would be reflected in SuiteCRM. Also, because importing and relationships would not be available in the external e-mail, all messages would have to be imported to the CRM and assigned to the user: while messages in TRASH would undo this.
So, the suggestion is to ideally to beef up the e-mail client, or at least make it play nicely with external mail clients.