This isn't such a bad idea but let's take something into consideration. Although I'm not sure it would be possible according to how the login and account system is currently implemented.
Nothing is keeping you form creating a separate account in the first place. So why would you create your account linked to this one once you already created it? It goes against your own statement :
not have people know who you are for certain sites
You let them know by creating your account on your current network profile.
This is a bit off topic but.. What is wrong with people knowing that you participate on other sites. That is if they even go there to check.