No, the coefficient is not equal to the loading. As it says in the help documentation "for the on Correlations option, the ith principal component is a linear combination of the centered and scaled observations using the entries of the ith eigenvector as coefficients."
If you use the Unscaled option (or if you use the Correlation option on already scaled and centred observations) the coefficients are just the eigenvectors. Otherwise the coefficients are the eigenvectors adjusted for centering and scaling.
I think the attached example might help.