why and how do you deal with "other undesirables" ?
I find linkedin connections number to be a key when talking to recruiter. they dont really care who I connect to, but rather a number of connections seems to impress them. for that reason, I would add anyone to my network. Also - one person that you may not know on LinkedIn may be linked to someone you would love to know!
I have a LinkedIn account and all I ever do on it is accept incoming connection requests. Other than that, I never ever use it for anything. Except maybe once a year to see if guy X who left the company found a new job yet.
Many connection requests are recruiters over here, too. I ignore those.