It all depends. "depend"=>"hang from"
But hang from what? In this case, what do you want to say on the InterWeb? Do you want others to say it for you, or argue (violently) against/for your wisdom (FaceBook)? Or chat to each other, and maybe you as well (Twitter)? Watch your magic and make--hopefully polite--comments (YouTube)?
Or maybe you'd like to quickly show people in an organised way what you can do for them, leaving room open for extra details as needed?
Having a website is no necessary precondition of existence, and the same is true of any other social media. But a website is a tool in a tradie's box, as are the other media. Look at it this way: in which medium can you totally customise your existence in a way that keeps people coming back? I won't bother illustrating the neo-classical social media, you know how miserably equipped they are as well as I do.
Your choice will be dicated by your clientele. Once you have a presence in Réalité, professional clients need only your superficial expression in Virtù. You don't have to tell them anything, so an instructive website is superfluous. But an amateur won't have the in-depth knowledge to know what questions to ask, and if you consider these lesser creatures worthy of your time, you do definitely need a website, and you should make time to keep your Social Experience well pruned.
I trust this has not made things worse?