NO, QTP will not create .tsr file while running the scripts. You should have relevant .tsr file to run yours script. This is the basic concept of QTP.
You can run in maintenance/update mode to change the object in .tsr file with the reference to the current application. Means, if your application objects property changes due to some development, you can update your already existing OR by running script in maintenance mode.
You can run in maintenance/update mode to change the object in .tsr file with the reference to the current application. Means, if your application objects property changes due to some development, you can update your already existing OR by running script in maintenance mode.