Just like any embedded device going off-line, will the browser too goes offline, if there is no user action for say for 15 minutes.
This will automatically save power for number of switches / router in between the machine and Webserver as well saving power at both Machine and Webserver too...
Currently any website works based on TCP based and hence there is continuous exchange of packets between website and Webserver.If there is no user action then the browser can go completely offline so that no packet will get exchanged.
Note: there must be provision such that the connection when restored should be able to resume without any issues.
This should not be applicable when downloads are started from a Web Browser.