As in subject. Is it at all to send and email with PHPMailer and assign different message-id for the mail sent to 'to' and do 'bcc'?
(Yes, I know is not exactly compliant with RFC nor is intuitive to do such a thing.)
No, because when you send a message using BCC, only 1 message is sent. If you want different messages sent to different recipients, send separate messages.
You can see this quite easily: if you add multiple to, CC and BCC addresses to a message and send it (with SMTPDebug output enabled), you will see all the recipients sent to the server using RCPT TO commands in SMTP, but that will be followed by just one message.