I use a free email provider which uses a browser based client
currently it automatically updates your inbox while you are online.
this means i can leave the browser window open all day and new emails will appear on my screen as they come
do the major modern email programs (ms outlook, opera, ect do this)
Are you asking if Outlook works through a web browser (yes it can through Outlook Web Access or OWA)?
If you mean, will Outlook automatically check for new mail and fill your inbox through the day then yes, it has always done this.
You can set the frequency that it checks for new mail in the preferences.