This is for an unpaid ticket for failure to possess drivers license.
Criminal Defense Attorney
Technically, yes they could, however, most police departments have much better things to do than round up traffic violators (but it can still happen and you should address it immediately). That being said, if you were subject to a traffic stop, you would likely be arrested. I would recommend hiring a lawyer, often he/she can be effective in lifting a warrant pending the next court date. Even if the attorney is unable to have a warrant lifted, he/she can advise you and walk you into the police station. If done right, the attorney can secure a reasonable bail immediately, without you having to go to the county jail.
DUI / DWI Attorney
You are more likely to be picked up on a warrant for a police traffic stop. This typically occurs at the worst possible time. Your best bet is to pay bail now or retain counsel in an effort to recall the warrant and defend the underlying traffic ticket in court. In addition, make sure that the NJMVC has not suspended your driver's license in response to the traffic court warrant. If your driver's license is suspended, you will need to pay the NJMVC a $100.00 restoration fee after your ticket matter is resolved in court.