From your descriptions it looks like a simple and not very intensive application. Based on my experience with Railo Express, I think you have the power needed to run this.
What I would do is to install the application on the computer at the counter since that is the main hub (you mention the iPad connecting wireless). Use the stick as a backup and before they take it home, make sure the stick is updated with data. You might also consider designed the app so that there is separation between writing data and consuming it (e.g. people at home running reports).
Will the app on the stick run at home, most likely it will work, or if you run into some problems will not be hard to fix.