No. A Google My Business page can be created and optimised in a way that may help your business show up in the Google maps ‘3-pack’ at the top of the page - if your competition is either minimal or non-existent.
BUT…
If you really want to see exponential growth in sales, leads and overall revenue it’s imperative that you have a website. You can have dedicated pages for all of the services you offer, each of your service areas, and grow it into something that will attract new customers by itself.
So long story short, sometimes you don’t need a website but if you do have one (we’ll even build it out for you) it’ll undoubtedly lead to higher local search engine rankings and better results overall.