Depends on your state. Most states are now on a federal network. These states honor each other on issues like this. They can refuse renewal of license and/or registration. Example of how far back this can go? A LONG FREAKING WAY! I lived in Tennessee in 1984. Got a ticket there. Paid it. I soon after moved back home. I had TN DL at the time, but stupidly never forwarded my mail properly. I later found out my license was suspended in TN. Got it straightened out and renewed my license in my home state. No problem....or so I thought.
Flash forward 24 years to 2008. I go to renew my current license. The lady does a check and tells me I have a hold on renewal because of an issue in Rutherford County, TN. That's all she can tell me. She gives me a number to call who tells me to call Rutherford County Court house. I google Rutherford County and see Murfreesboro, TN adn that ticket in 1984 comes rushing back. So I call them. The woman tells me she has to go to the basement into a file cabinet to get the history on it. she is laughing because like me she can't believe this. She calls me back 2 hours later and explains that I owed them a reinstatement fee that was never paid. Keeping the story short as possible I asked about statute of limitations. She stated that that would apply if this were a fine, but it was a renewal fee and that I would have to contact the state of TN Dept of Transportation to clear it up. I call them and find that over 24 years the $25 reinstatement fee with interest and late fees was currently $297.00 and that they accept all major credit cars. Needless to say I paid the fee, received the release of hold letter in the mail, and got my license renewed. I came to find out that Tennessee had just gone on some federal network sharing interstate information like this in 2007 that most other states were already on.
Yes you will likely end up having a hold on registration or your license renewal if you don't pay them out and interest can build up along with late fees.