Yes, you can access your mail from both Outlook clients.
The reason for this is that the mailbox is the same mailbox. Think of it this way: you have a mailbox in your front yard. You can go out and check it, or your friend can go out and check it, and it will always have the same mail in it.
Now, another thing that is going to come into play is what Protocol you are using to check your mail. Usually, you are using POP. With POP, the mail is deleted as soon as you read it. This means that the first Outlook that sees it gets it. If you see the email with your home computer, your work computer cannot read it because now it is gone (taken out of the mailbox). But Outlook has an option under 'Advanced Settings' called 'Save a copy of messages on the server' to get around this. As long as you have that setting checked, you can see your INBOX from any computer that has your POP settings on it. Any sort of mail rules, special folders you create will be present ONLY on the computer you set those rules on.
Now, you can also use IMAP. IMAP works similarly to POP in that it lets you check your mail. However, IMAP maintains a connection to the server. So, its always looking in the mailbox. If you have folders created for storing mail you can create them as 'IMAP folders'. Any computer connecting with IMAP will see those folders. IMAP does not automatically download mail off the server because it it always checking the server (different from POP, because POP just grabs mail off the server). A lot of free Webmail Clients use IMAP.
Another Protocol is Microsoft Exchange. With Exchange, EVERYTHING you set up in Outlook is shared across any computer you connect with. This includes rules, address books, calendars and other functions. It is similar to IMAP in that it is always connected to the server. Also, many mobile devices can connect to Exchange mailboxes as well, such as Blackberry. The drawback to Exchange is that to use Exchange, your mailbox must be created on an Exchange server running Microsoft Exchange software. POP/IMAP is usually free, whereas Exchange is very expensive. So, it will cost a fair amount of money to implement Exchange.