Yes, if you create a routine with the phrase “Good Morning” it will override the built in response. It can take a short time for the routine to start working, so if you try immediately after setting it up you may still get the default response, but give it a minute or two and it should work.
Incidentally, if you want to create a routine which overrides the “Good Night” response you may need to use “Goodnight” as the phrase instead of “Good Night” as I did.