In theory, yes. OneCare installation and activation is not very forgiving of connectivity issues, unfortunately. My suspicion is that you may be using the AOL web browser as the default web browser, which can also cause issues.
You also want to make sure that no other security software is installed as that will cause problems with OneCare moving forward.
OneCare will check for updates in the background throughout the day when you are connected and will download them in the background. About once per month, the virus signatures/firewall rules database will be refreshed. This can be a fairly large download and will require that the connection remains open for a reasonable amount of time (not the 3 hours you encountered for the original installation). If OneCare cannot update, the icon will turn red and will advise you that the PC is at risk. You'll want to review this post in that case:
http://social.microsoft.com/forums/en-US/onecareupdate/thread/9a6a0003-b91c-4518-966c-fc50450f0e41/
-steve
Microsoft MVP Windows Live / Windows Live OneCare & Live Mesh Forum Moderator