Can I make chicken pot pie with mashed potatoes inside?
Generally such a concoction (topped with mashed potatoes) is called a Shepherds Pie, but adding a crust... I have no idea what to call that ;-)

When cooking a pot pie everything is already cooked prior to putting it in the baking dish, except the crust. 

So all you really need to do is make sure your crust is cooked to your desired done-ness. The mashed potatoes might keep the bottom of the crust a little wetter but really it should not require much more than you usually would bake it for, if any. It depends on how hot you bake your pot-pies.

I usually cook them at 425F so I get a nice brown on my crust and it is about 15 - 20 minutes, but that will depend on your crust recipe. I would follow the crust recipe baking instructions and add maybe 5 minutes.

You can then try the pot pie and adjust the backing duration according to your personal preference.