I recently upgraded to Flutter 2.0. I have dozens of Flatbuttons that are now deprecated. It's going to take me a few days to fix them all. What are the consequences of shipping an update before then with deprecation warnings? The app still builds and runs fine.
Basically this code will be deleted in future releases of flutter/flutter packages. Most of the time, api's get deprecated when a bug that requires a completely new implementation that will break compatibility or a better implementation that will break compatibility.
Therefore, you can use deprecated code but you should be very careful as they are not maintained and might stop working or deleted in the future. So as long as you are not updating versions you should be fine but it is highly unadvisable.