I guess it depends. I'm not really good at relationships, but I can be a very normal guy in almost every scenario. So, I'm not like asking my manager what did he do during the weekend (but if he talks about it, I listen and follow the discussion), nevertheless he's a professional and if I do my job the way they like it, I'll get a promotion (if I don't, then I need to switch to another company).
Similarly, I'm not friend of my work colleagues, but I'm definitely not a dick. It's easy to not be a dick; it's not easy to be "friendly".
I don't have a work network at all. The people I have worked with in the past are Linkedin connections now (I do have the phone number of a couple of people, though), but I have never relied on them to get a job (among other things, because they live in different cities, countries and continents).
So, many of us are doing just good by being really really minimal social beasts. I think the key is to not being a dick, but that doesn't require being a social person in my experience.