Hey Gal,
Adding a WhatsApp banner with such purpose to your site is definitely possible. You can use a ““click to chat”” feature provided by WhatsApp, which generates a unique URL that you can add to your website. When a user clicks on the banner, it will open WhatsApp on their phone and start a chat with your number.
You can also use a plugin or widget that is available for website builders like WordPress, Wix, Shopify etc.
As an alternative, you can also use https://freetring.com for creating such feature.
Let me know if it was helpful!