Any driver's license that isn't beyond the expiry date will suffice here for the average traffic stop. As mentioned, officials here can't easily check it's validity. Here the officials are looking for a reason to get you to pay them and your foreign license serves only to establish that you do not have a DR license therefore you have to be legally in the country to drive using that license.
Some of the the big US affiliated rental car agencies may have the ability to run your license to ensure it is at least valid.
Now if you get into a traffic accident, that will be a different story. As part of the investigation and we shouldn't have to remind you that foreigners are put on a short leash during investigations, your license info could be sent off for validation by US authorities. No license, in an accident, probably not a good idea. No license means, no insurance, rental car charges and any penalties assessed by the DR.
Driving here is riskier than at home especially for those not used to the roadway chaos. You can take a lot of taxis for the cost of a rental car.
Those who opt to commit an offense (let's just say in this case your US license is invalid for some reason) in a third world country are just asking for a world of grief.
In the event you are just asking to see if the authorities were able to run your license if you were stopped here previously, no they can't and they will not be notifying the dept. of motor vehicles in your state that you were stopped/and or ticketed.