I wanted to use this to keep track of which cards I have and maybe what box I keep each one in. Is that possible with this app? Maybe I'm using it wrong, because it does not appear to let me do that.

You edit your inventory for what cards you have. To do so, click Edit and add it there, or if you are in an advanced search results view with a list of cards, click the green box to bring up the same popup window.

However, there is currently no way to add notes to a card to keep track of what Box it is in though.

I'm sure you can use the deck building tool for this.