It is unlikely as the data base used by the TSA focuses on more serious crimes. That said, no one can promise you that you can travel with impunity while you have an outstanding warrant. These are times of heightened security and the screws are being tightened. If I had an outstanding warrant I would not attempt to get on an international flight. Tkae care of your problems at home first.
You need to address the warrant for the DUI regardless of whether you intend to travel internationally in the future. Otherwise you're going to forever have concerns like these about being detained or arrested.
Depending on which Judge your case is in front of, an attorney may be able to appear for you without you present to get the warrant vacated and address the underlying DUI charge.
The fact that you have an open warrant it is possible to be arrested for it. This is especially true if going through customs. The best advice is to clear up the warrant. Get this monkey off your back.