Yes. You can get the status, but you will have trouble renting a car outside of NY and MI (which by law must rent to under 21) unless you have a CDP that allows for underage rentals (like USAA, IBM, Siemens, etc... AAA is only for 20+).
When you use those CDPs you will likely be asked for ID anywhere in the tristate, Miami, LA, Phoenix, etc. (Basically wherever there are a lot of Bochurim trying to use CDPs)