The Ellacoya SP website doesn't say anything but they don't really list the rules. You can call them.
http://www.nhstateparks.com/ellacoya.html
The Gilfrod town beach has this in the rules:
"Access to this facility by any other means (boat, ATV, fence jumping, etc.) or failure to stop when directed by the Attendant may result in immediate expulsion..."
You could easily drop her off at the Alton, Center Harbor or Weirs beach public docks and she could walk to nearby beaches.