Can you have a warrant without being arrested?

If you press charges against someone, and if in the process the police discover that you have a warrant for your arrest that remains outstanding, they have a duty to arrest you. Whether they will necessarily check you out to see if you have a warrant for your arrest is another matter. That does not always happen as a matter of course. However, there is always the risk that they will do so and you would typically be arrested on the spot.

Added; In most professionally administered law enforcement agencies it is standard practice to "run" the names of EVERYONE involved in a case through a criminal history computer check.