Gentry and Wellum point out that this is true. The word does not appear until Gen. 6:18. It then reoccurs in 9:8, 11, and 17. The argument which they make deals somewhat with the language used in Hebrew covenants. I quote now from chapter 5 of Kingdom through Covenant:
There is a conventional language for initiating covenants or treaties which is standard in the Old Testament. The standard expression for initiating a covenant is “to cut a covenant” (kārat bĕrît; 21:27, 32)...Animals are slaughtered and sacrificed. Each animal is cut in two and the halves are laid facing or opposite each other. Then the parties of the treaty walk between the halves of the dead animal(s). This action is symbolic. What is being expressed is this: each party is saying, “If I fail to keep my obligation or my promise, may I be cut in two like this dead animal.” The oath or promise, then, involves bringing a curse upon oneself for violating the treaty. This is why the expression “to cut a covenant” is the conventional language for initiating a covenant in the Old Testament.Although I don't want to spend the post getting into the arguments behind the next assertion, I will summarize it by mentioning that the word used in Genesis 6:18; 9:9, 11, 17 is not kārat bĕrît; rather, the phrase used is in reference to the covenant with Noah is different: "hēqîm bĕrît." With Noah, God is not cutting a covenant, but rather, upholding a covenant.
...the expression “to establish a covenant” (hēqîm bĕrît) refers to a covenant partner fulfilling an obligation or upholding a promise in a covenant initiated previously...The implications are a pretty big deal. It means that when God "establishes" his covenant with Noah, he is really simply upholding a pre-existing covenant. What covenant could this possibly be referring to? Well, of course, it is the covenant of cration, began with Adam. Noah was not the first person whom God made a berith with but rather, it was Adam. Wellum/Gentry offer a summary:
...based on the expression hēqîm bĕrît, linguistic usage alone demonstrates that when God says that he is confirming or establishing his covenant with Noah, he is saying that his commitment initiated previously at creation to care for and preserve, provide for and rule over all that he has made, including the blessings and ordinances that he gave to Adam and Eve and their family, are now to be with Noah and his descendants. This can be substantiated and further supported by noting the parallels between Noah and Adam, and between the covenant terms given to Noah and the ordinances given to Adam and his family.Wellum/Gentry summarize the parallels between the covenant with Adam and the covenant with Noah:
Covenant with Noah: be fruitful and increase in number
Covenant with Creation: be fruitful... (Gen. 1:28)
Covenant with Noah: Fear of you
Covenant with Creation: Rule over fish, birds, animals (Gen. 1:28)
Covenant with Noah: Animals given for food
Covenant with Creation: Plants given for food (Gen. 1:29)
Covenant with Noah: Don't eat meat with blood
Covenant with Creation:
Covenant with Noah: Your blood... his brother's life
Covenant with Creation: See Gen. 4:8-24
Covenant with Noah: In the image of God
Covenant with Creation: Gen. 1:27; in his own imageWellum/Gentry devote an entire chapter in Kingdom through Covenant to this argument, and at this point the book appears to be worth the price simply for this chapter alone. The book went on sale on Friday. You can find it at Westminster Books.
[Edit (7/4): Upon reading the comments, I realized that I had misrepresented Gentry and Wellum's argument. I changed two words in the post in order to correct this. I had originally said that G/W believe that the Noahic covenant is an upholding of the covenant of works. I had meant to say that they believe the Noahic covenant to be an upholding of the covenant of grace. That would have been a pretty huge error.]