No, we cannot say that all elements are an "energetical incarnation." While it is true that the number of protons determines the atomic number and, therefore, the identity of an element, the concept of an "energetical incarnation" is not a scientifically recognized concept.
The properties and behavior of elements are determined by various factors, including the number of protons, electrons, and neutrons, as well as the arrangement of these particles within the atom and their interactions. Energy plays a crucial role in these interactions, such as in chemical reactions and nuclear processes, but it is not the sole determining factor for the identity of an element.
The classification and understanding of elements in chemistry and physics are based on the periodic table, which arranges elements according to their atomic number and organizes them based on similar properties and trends. While energy is involved in the transformations and interactions of elements, their identities are primarily defined by their atomic structure rather than being solely attributed to energy.