Yes, the way the toll systems work in the following order. Transponder first, if it reads a valid transponder nothing else happens. The plate is run through the local tolling authority to check for a match, Visitor Toll Pass, SunPass or E-Pass in Florida. Still if no hit, the plate is run through EZ-Pass. If still nothing, the plate is run through PlatePass. As a last resort the plate is run through the state's DMV and most but not all states will give FL the owner's information. MN and a few others will not.
I've never had an issue with my transponder not reading, but I always mount it exactly where I do in my own vehicle. Could be an issue with newer vehicles or people mounting it differently.