Kupka-Smale plus $h(f) >0 $ forces homoclinic points.
See M. Herman, Construction d'un diffeomorphisme minimale d'entropie nulle, Erg. Theory and Dyn. Syst. 1 (1981) 65-76
In dimension >2 the answer is "no": the product of any diffeomorphism f by an irrational rotation (or translation) as no periodic points, hence is Kupka-Smale, but has the same entropy as f (hence it can be >0).