Yes, you could set your Outlook to remove messages from the server. Anytime a message is sent to Outlook it will delete the message from the server. If Outlook is closed, emails are grabbed by your BB as well, AND waiting for Outlook the next time it is opened.
Do just the opposite of the instruction in this link... Some email comes to my BB and some does not - BlackBerryFAQ
good luck, AND welcome to the Forums.