Can I add a pop up drain stopper to this bathtub?
You can replace the silver drain spud ( the silver part in your tub )  by using  this special tool. You can replace it with one that will accept the stopper you have or any other. 

You place the tool into the spud and use a crescent wrench or a screw driver thru the hole to gently turn it counter clockwise to unscrew it from the drain pipe under the tub, then install the new one in the reverse. 

Use a little lube on the new treads and some plumbers putty under the flange when you put the new one in. There is a gasket under the tub between the drain pipe and the bottom of the tub, this should stay in place but be careful not to let it fall down inside the space under the tub.