Hi. If you are having this problem you don’t need to turn off the mail service – you just need to change the email routing setting so that it knows that Google is handling your email. See this article for a more thorough explanation:
https://teachyourselfgeek.com/google-apps-business/dont-receive-email-contact-form/
…on the other hand – you might decide it’s advantageous to turn off the mail service to save resource on your server – since Google is handling your email anyway.