Since you asked, I think so yes, though i wouldn't give this opinion without your question. Parents know what's best for their children!
I may be old fashioned but I think 12 is an age to be learning real social skills, not just virtual ones.
It's a time to play games with other children, and not on play stations or computers, though some time on those is very useful and fun.
Social networking gets adults hooked; lots of us wished we weren't spending so much time networking. It's quite addictive. Anything addictive is very bad for a 12 year old, who has not yet learned how important it is to 'control' unhealthy behaviors. In fact, through interacting physically-socially, young people learn lots from each other; what's acceptable behavior, what isn't, what's going to get a laugh from friends, what's going to get you left out, what is obsessive, what is lazy etc.
Through being together, 12 year olds prepare how to be 13 year olds and so on. Taking time away from 'being together', through social networking, might make a 12 year old network savvy, but it will probably take away from learning how to live life 'out there', where real life still gets lived.
If the social network is done for a certain amount of time each day, and only for this time, then I doubt there's a problem.
The problem is getting the 12 year old to stick to this time 'limited' frame! If you can do that, why not? Ours is a very virtual world isn't it?