I do not know if the DOT checks for warrants when an ID is applied for. You could call anonymously to the local office and ask them if that happens. Do not give your name or any identifying information. You could tell them you are doing a research project, which technically you are for yourself, and need to know that but you cannot lie to anyone about anything.
I cannot answer your direct question, but you are almost always better of dealing with an outstanding warrant on your own terms rather than being picked up by surprise and then trying to convince a judge that you can be trusted to come to court on your own in the future.
Ideally you should have an attorney arrange for your appearance in court to address the warrant, preferably with something acceptable in terms of bail or release conditions worked out with the prosecutor in advance. A court is much more likely to set aside a warrant or to issue a reasonable bail amount if you demonstrate that you will appear in court to address any pending charges.