Leaving the DNA behind doesn't really identify him if his DNA is not in the system.
But nowadays the odds some relative of yours put theirs up on some family tree site is pretty high so they could narrow the suspect pool quite a bit going that route.
This is a classic tactic cause you can scan them without scratching them at the store and filter out any actual winners and just leave people with essentially nothing.
When I worked as a cashier there was a real estate agent who bought scratchers all the time and did exactly this. If one of them won more than like 50 bucks he cashed it and took all the worthless/low value ones. Then all his clients would get them in the mail for Xmas.