There are problems, I shall list some of them:
1) In special relativity, relativistic energy concept is not coming from consideration of elastic collisions. In fact, relativistic energy is a covariant generalisation of non-relativistic energy. As a viable approach to do this one may generalise the action for a free particle first, and then derive relativistic 3-momenta from lagrangian and energy from hamiltonian. The point I want to stress is that no collisions are needed for derivation. In contrast, covariant generalisation procedure is crucial.
2) You can link the energy of the particle to the energy of the whole ensemble (even a non-relativistic one). However, as you cannot derive the relativistic energy of a particle from a single collision, you cannot do that for a collision with an ensemble.
P.S. On the contrary, if you think that you can 'derive' relativistic energy from 1 collision, you shall then be able to do it for collision with an ensemble.