As someone who gets up early in the morning to go online -- and, yes, as someone whose online habits have sometimes (OK: regularly) impacted my attention and time for my kids in the morning -- I cannot judge parents who spend a lot of time online in the early morning.
I will say that "online-offline balance" feels like the new "work-life balance." I think this NYT story today just legitimizes something that has already been going on.
Again, it's not necessarily bad -- unless you are spending your entire early morning focusing on your fantasy team and Twitter stream, rather than parenting your kids.
I will suggest what I have tried to do: Get up 15 minutes earlier -- you'd be shocked at how much online consumption you can get done before your kids need your attention.
If you want to discuss, head over to Varsity Dad.
(If you don't have kids, of course, you have all of your time to yourself, anyway.)