It is a possibility but one should bear in mind that there were many other people also named "William P. Heath". Here are some examples from the 1930 census:
William P. Heath, born about 1920, living in Los Angeles, CA
William P. Heath, born about 1918, living in Santa Clara, CA
William P. Heath, born about 1875 in Indiana, living in Denver, CO
William P. Heath, born about 1876 in Georgia, living in Buckhead, Fulton, GA (this is our Heath, Sr.)
William P. Heath, born about 1877 in Georgia, living in Dug Road, Pickens, GA
William P. Heath, born about 1928 in Georgia, living in Dug Road, Pickens, GA
William P. Heath, born about 1872 in Kansas, living in Neosho Falls, Woodson, KS
William P. Heath, born about 1902 in Tennessee, living in Newport, Campbell, KY
William P. Heath, born about 1871 in Kentucky, living in Durbin, Edmonson, KY
William P. Heath, born about 1877 in Vermont, living in Rockland, Knox, ME
William P. Heath, born about 1916, living in Fryeburg, Oxford, ME
This is only about a third of them....and this is not even counting those just listed as "William Heath" but who may have had "P." as their middle initial.
To disconfirm your hypothesis, try to find if this William P. Heath was born between 1930-1939, and if he was born in South Carolina or Georgia. If not, then he would clearly not be relevant to our Heath, Jr.
I was also thinking of contacting the Coca-Cola company if they have an institutional historian. William P. Heath, Sr. was the Vice-President of Coca-Cola. Surely, there'd be stuff on that!