No. You are assuming a philosophical definition for science that science cannot methodologically validate. You are free to proceed with your assumption as to what defines science. In most cases your methodology and conclusions will not suffer. But when you argue from the details of your methodology into the bigger scheme of things your philosophical stance, for better or for worse, will guide the explanation.
The philosophical definition of science doesn't have to be methodologically validated. The definition of science is the definition of science. Philosophical naturalism and methodological naturalism are not the same.
A desire to consider the supernatural within the rubric of science in now way changes the definition of "science" any more than the homosexuals' desire to marry each other changes the definition of "marriage."
I believe that you are proceeding from the misconception that "science" is something more than it is, or that a scientific statement or conclusion is more than it is. A scientific truth, for lack of a better word, is merely a conclusion reached through the scientific method; i.e., it makes a statement about the natural word, as informed by natural phenomena and facts of nature. By definition, it cannot say anything about the supernatural.
Science is not a search for ultimate Truth, or the meaning of life, or some such. It is just the application of the idea of the scientific method to the natural world. That's it. If I were to conclude that this means that there is no God, or that there is a God, or anything like that, then that conclusion is as unscientific a statement as they come. Once you add anything supernatural in there, it ceases being science. Maybe you are doing a scientific-theology, if such a beast is even cognizable, but it is not science.