Which version of Exchange are you running?
You can setup email however you want. I personally use 1 email address in one of my installs.
Admin Panel -> Settings -> Email Settings
I have:
Incoming Emails:
Enable POP/IMAP email fetch
Outgoing Emails
tickets@domain.com
Default System Email:
tickets@domain.com
Default Alert Email:
Use Default System Email (Above)
Then if you go to Admin Panel -> Emails there is only one email address in there. [ie tickets@domain.com If you edit it, I've configured it to use IMAP. The username and password that you enter on this screen MUST be a legitimate Exchange username and password. So yes you have to setup at least one account in Exchange.
Our "customers" send email to tickets@domain.com to open a ticket, or goto the web page.
You can add more emails and departments. For each you add you have to have a corresponding entry on your DC/Exchange server(s). Or if you dont care about checking those mail for tickets and want to funnel everything through one account, you could use distribution lists for the departments.
I personally would create a new email account for the new ticket system. Why? Because depending on how you have OS ticket configured it will email you (or a distribution/security group when tickets are opened). If people go into that account and delete emails prior to them being tossed into the ticket system no ticket would ever be opened. How often do you really want to run cron? We run every 2 minutes currently.
I think that covered all of your questions... :)
edit: oh yeah nearly forgot. Our New Ticket alerts get sent to a distribution group so that all of our support personnel receive a copy of the new ticket.