That definition is a defintion only for the purposes of a particular statute, and it does not attempt to redefine a Constitutional term just because “it’s not defined in the COnsitution.”
Lack of any other response confirms, that in your bizarre theory, the Congress could define the “navy” for Constitutional purposes as “lollipops” if they were so inclined.
Considering that Title 10 (i.e., National Defense Act of 1947) is basically the only logical place to do so, you are right.
And you are right on this part, as well. If they decided to create a definition in Title 1 of the US Code, one that would apply for all the remaining titles, they could do so...even if they wanted to define the Navy as the Land Service. If POTUS would sign such a silly definition, it would apply.
Like it or not.