Yes you can – but why would you want to? It’s not advisable for a few main reasons.
Firstly, as popular as Social Media Channels are not everyone uses them and even those that do on a regular basis may not do so to find a product or service. Fact is, the Search Engines are the number 1 go to.
Most people looking to employ the services of or buy from a local business expect them to have a website.
Why not cover all your bases, having a website doesn’t mean you should ignore Social Media and vice versa.
It is unlikely but any Social Media platform is a 3rd party application. What would happen if you invested all your time in promoting your business on a social media platform that one day no longer existed?