If I use a store brand premade pie crust would it jeopardize this pie’s ability to stand up straight, as shown in the picture?

Yes you'll likely have problems doing the deep dish pie with a shaped store-bought pie crust.
But there is commercial pie dough sold in flat or rolled packages, which you can shape yourself to fit the dish you are making.
Look for one of those formats near you...either in store frozen or refrigerated cases.