Hi 11qa,
I am not clear on this as I have not previously worked in a police department. However, I suspect in a simple license check, they are able to see if the license and car registration is valid, if not, the duration of any suspension, if valid, what type of license it is and any special conditions imposed on the license (e.g. requiring vision correction to drive or if able to drive larger vehicles), whether the registration has any issues with it (e.g. any person reporting the car stolen). If a person is under an outstanding warrant (e.g. wanted by the police or court), they are most likely able to see this through a intra-state or inter-state police alert.
I suspect they do not see your full criminal history or other traffic infringements (but may see any current offences, e.g. if you are on probation). Such information should not influence the police in whether to charge you for a current traffic infringement or not (unless you are on probation). This decision should be based solely on the current set of events. However, the police will have access to your criminal history (and past traffic infringements) later once they run a more detailed police check on you. This will then influence their charge (if it is not minor) and what sanctions they seek.