It is technically possible for you to implement your own cart into PowerStore but it would not be an easy task. The eCart integration handles all of the cart and checkout options, so if you worked with your other cart you would need to re-create the entire checkout experience as well including storing the order information in your db.
When you are using PowerStore there is no need to do any cart based editing, when you add items to your admin backend the items will be available in the store without doing anything further. The code is all dynamic and does not require you to make any changes to get your items available in the store, I think it may be simpler to just use PowerStore by itself if this is an option for you.