Technically, no. Definitely not on Object Bar.
I am using FF as my default browser with the FasterFox weather extension. However, by default the extension is disabled. Also, I changed it's update to something like every 2 hrs. The extension was not running when I noticed the 5 minute internet access request.
My use of OB is limited to two additional bars: a top dock straight from the Dogma4 skin/theme and a left dock autohide arranged as series of folders with games & game utilities, the Programs & My Documents folders on it.
Nothing else is on OB. Nor do I run a desktop / systray weather application. Nor anything else in either location that is new or shoud be checking the internet regularly. (I should mention that I do not have internet access at home so I don't use such "features" in most software.)
It was trying to access 66.28.242.218 which is Cogent Communications. BTW, while writing this message, DXwidgets.exe asked for permission to check the internet as well.