There are two separate features of Gmail, that when used together can greatly ease the management of multiple email accounts.
Firstly, setup a mail import using POP3 and select the options “Archive incoming” and “Label incoming”. This will have the effect of labelling all your mail from that account (call it “Account1″) and more importantly NOT displaying it in your regular Inbox.
Now for the magic, go to Gmail Labs and enable “Multiple Inboxes”. At its base this tool simply allows you to have multiple panes above or below your regular Inbox, and the contect of each pane is specified as a Gmail search (can be keyword, label, or anything else).
So set a pane’s search as “is:Account1″, and the mail that is imported by POP3 will show ONLY in this pane, and you can check it at the same time you are checking your Inbox.
References
How to use Gmail’s “Multiple Inboxes” for extra Gmail accounts