Of course, you need the raw cognitive power to solve problems. But at the high-end of consulting, clients already assume this to be this case (otherwise they wouldn't be spending $200+/hour for people fresh out of college). What clients are looking for is more akin to a 'trusted advisor'[1]. Someone they can trust and rely on.
Yes, you can be socially awkward and still get the job done. But you probably won't be considered when the next opportunity arises; what people value are relationships. If you've got that (and you have the technical chops), clients will tend to keep calling you back for years to come. Or perhaps mention you to their peers.
For anyone considering working independently, I highly recommend David Maister's books. He writes clearly on earning trust, the art of listening, providing advice, establishing relationships, and so on.
This is really what separates the engineers who can command top dollar for their skills in the marketplace--versus those who are viewed as just another number on a spreadsheet to minimize (in the eyes of management at most large companies).
[1](http://www.amazon.com/The-Trusted-Advisor-David-Maister/dp/0...)
I'd recommend reading The Trusted Advisor [1]. It was originally written with management consultants in mind, but it is a good guideline in general for how to walk the line between personal and work relationships. Basically, you should look at your clients as you would a friend: be their friend, know their problems, and help them with those problems. Become invested in them and their success, and they will invest in you. Business is ultimately about people, but I feel many technical workers focus on the technology and get screwed over as a result.
[1] http://www.amazon.com/The-Trusted-Advisor-David-Maister/dp/0...