No!
I cannot understand how any thinking person could believe an American organisation or law enforcement officer will be forced by an American court to respond to a foreign demand for this type of enforcement. (But we are talking about unelected EU officials here, so they may not actually belong to the 'persons' subset that the rest of us do.)
This type of reciprocity has never happened in the past, America has never accepted that external treaties and agreements actually have any legal basis in their judicial system. They, of course, hold full sovereignty over the entire globe.
If the negotiators believe that this agreement is fair and equitable, then they are deluded fools.