No! You do not need to return your completed marriage license back to the clerk together. You don't even have to take the marriage license back in person - they allow you to mail it. Anyone can return a marriage license to the clerk's office.
Indiana marriage laws state that the wedding officiant is responsible for returning the marriage license to the clerk. This is not really enforced. Usually, couples return the marriage license themselves. It's easier.
Some counties include certified copies when you pay for your marriage license when it is issued. You can mail your license to them and they will automatically mail certified copies to you.
Other counties do not allow you to pay ahead for marriage license copies, they require you to request and pay for the marriage licenses after you are married. If your wedding officiant returns the marriage license, you still need to request and pay for copies. It's usually easier for you to do that.
My office is in Marion County and the Marion County Clerk requires you to request your copies after your wedding. If you book a wedding with me that costs $150 or more, I will return your marriage license for you and mail you two certified copies. I include that in the package. I walk from my office to the clerk every Monday to return licenses. This is super-convenient for Marion County residents. The surrounding counties are usually much more accessible with free parking and no downtown traffic. It will take you a matter of minutes to return the license and get the copies directly in your hands.