The structure and energetics of exciplexes M*((2)L)He(n) (M = Cu, Ag and Au; L = P and D) in their vibrational ground state are studied by employing diffusion Monte Carlo (DMC). Interaction potentials between the excited coinage metals and He atoms are built using the Diatomics-in-Molecule (DIM) approach and ab initio potential curves for the M((2)L)-He dimers. Extending our previous work [Cargnoni et al., J. Phys. Chem. A, 2011, 115, 7141], we computed the dimer potential for Au in the (2)P and (2)D states, as well for Cu and Ag in the (2)D state, employing basis set superposition error-corrected Configuration Interaction calculations. We found that the (2)Π potential correlating with the (2)P state of Au is substantially less binding than for Ag and Cu, a trend well supported by the M(+) ionic radiuses. Conversely, the interaction potentials between a (n - 1)d(9)ns(2 2)D metal and He present a very weak dependency on M itself or the projection of the angular momentum along the dimer axis. This is due to the screening exerted by the ns(2) electrons on the hole in the (n - 1)d shell. Including the spin-orbit coupling perturbatively in the DIM energy matrix has a major effect on the lowest potential energy surface of the (2)P manifold, the one for Cu allowing the formation of a "belt" of five He atoms while the one for Au being completely repulsive. Conversely, spin-orbit coupling has only a weak effect on the (2)D manifold due to the nearly degenerate nature of the diatomic potentials. Structural and energetic results from DMC have been used to support experimental indications for the formation of metastable exciplexes or the opening of non-radiative depopulation channels in bulk and cold gaseous He.