Is it possible for my python web app to provide an option the for user to automatically send jobs to the locally connected printer? Or will the user always have to use the browser to manually print out everything.
If your Python webapp is running inside a browser on the client machine, I don't see any other way than manually for the user.
Some workarounds you might want to investigate:

if you web app is installed on the client machine, you will be able to connect directly to the printer, as you have access to the underlying OS system.
you could potentially create a plugin that can be installed on the browser that does this for him, but I have no clue as how this works technically.
what is it that you want to print ? You could generate a pdf that contains everything that the user needs to print, in one go ?
python web script send job to printer