Not even close! I only have experience in the Gulf but they use "allah" words all the time!
"Alhamdulillah" (thank god) is pretty much part of the standard greeting (Pretty much just two people rapid firing a list of phrases at each other simultaneously "peace be with you / and also peace with you / how are you / thank god / how's the family / thank god") and a frequent response to almost any question.
Anything dealing with the future or uncertainty will bring in "Inshallah" (God willing). I remember the first time I asked my cab driver to take me to my destination and he said "Inshallah" that did not give me confidence!
Then there's "bismallah" and "mashallah" which I heard a bunch. And I'm not sure if we can count "yallah, yallah" which is like "hurry, hurry, let's go" which you hear all the time and is derived from "Ya Allah".
I would be willing to bet that Gulf Arabic speakers say "Allah" literally at least 10x if not 100x more than Americans say "God".