You can link a non-Gmail address to your Google account by adding it as an alternate email address. When you do this, you can do more than sign in to your account with this address too.
You can respond to invitations sent to your alternate email address right from Google calendar. People will see your Gmail address listed instead of your alternate address when you respond. As long as your Gmail address isn’t offensive and others can make the link then you should be fine.
Why would you want to do this?
For me, I wanted to use Calendly but it works best when integrated with a calendar. I didn’t want to create a new Google account. And I didn’t want to confuse things by asking people to send calendar invites to a separate address. I want a simple life.