Yes. It was in fact the mandatory greeting from 1933 until the end of the war and, especially in the later years of the war, not responding to a Hitler salute in kind was considered a criminal offense that could land you in a bureau of the Gestapo for a couple of hours.

I once read an excerpt of a diary by Victor Klemperer who noted in September '41:

„Man zählt, wie viele Leute in den Geschäften ‘Heil Hitler’, wie viele ‘Guten Tag’ sagen. Das ‘Guten Tag’ soll zunehmen.“

(my translation:) "One counts, how many people in the stores say "Heil Hitler" and how many "Good day". "Good day" is apparently on the rise."

(Quoted after: Klemperer, Victor: "Tagebücher 1940-41", Berlin 1999, p. 157)

The usage of the Nazi salute seems to have been used frequently while the common people supported the government but declined when the war kept on going and made a turn for the worse. This would explain the harsher punishments for not using the Nazi salute in later stages of the war when war exhaustion was growing rampant and the Nazi leaders couldn't be sure of popular support anymore.

The Wehrmacht meanwhile didn't use the Hitler salute but rather their old military salute - until the assassination attempt of 1944, after which the Hitler salute was made mandatory for soldiers as well, apparently to ensure their loyalty to the Führer.