Two separate push buttons for front door

I have two push button door bells for our front door. The outer is located next to our courtyard gate and the inner, adjacent to our front door. Both are connected to a chime inside the house. My question is: Can the Ring Pro be integrated to replace the push button next to our front door? When the button is pressed on the unit next to our courtyard gate, will the Ring Pro record video of the person entering our courtyard?