Yes, it will reflect the new subscription status on all PCs that are on your subscription. It can take up to 24 hours to show the new status after renewal. If it has been more than 24 hours, open OneCare on the PC that is not reflecting the new status and click Check for Updates. That should bring the new status down from the server. If that doesn't work, verify that the date and time on the PC are correct and contact Support for more help, if needed.
How to reach support (FAQ) - http://forums.microsoft.com/WindowsOneCare/ShowPost.aspx?PostID=2421771&SiteID=2
-steve