No, the 2FA app has no knowledge of whether you've used it or not. It just passively displays codes related to a particular timestamp and encryption key. It's essentially an elaborate clock.
If you open the 2FA app, its codes will keep changing as the clock ticks, regardless of whether you've used them.
SMS on the other hand DOES give a trail every time it is used. It is also insecure and much easier for hackers to spy on.