Other than the similarity of their names, it is unlikely that the William McBee whose grave marker you found is the same man who served in the 11th Arkansas. He appears to have worked for a time as a civilian contractor for the commissary department, but there is no evidence that he ever served in the army.

Samuel Hannah Cochran (1825-1877) enlisted in Blocher's Arkansas Battery at Little Rock on January 15, 1863.