At the particle level all interactions and decays are primarily studied at the center of mass inertial frame. Any potential energy does not affect the basic interaction. To see the effect of potentials on the resultants of the interaction in the original frame one has to do the reverse the Lorenz or General relativity transformation on the products.
For example take a muon decay in the center of mass.
Its lifetime is in microseconds and the energy divided into the three particles is of order MeV. Of the decay product only the electron is easily detectable.
Cosmic rays arriving at the top of the atmosphere(see paragraph 6) of earth generate very high energy muons some of which do not decay because the Lorentz transformation extends their average lifetime in the earth inertial system. The decay will divide up the incoming high kinetic energy too. Any potential that a top atmosphere muon had will be gained by the end product particles fall to the surface.
What if the object was emitting sound
Sound is a phenomenon of energy dissipated in moving molecules in the air. At the particle level that decays and elementary interactions occur,as the particles are either point particles or composed of point particles any interaction with the air molecules may dissipate part of the products energy as they keep falling. Energy will be lost by the electron, in the example, interacting electromagnetically with the density of air, which effect has to be included in the calculations for the original energy of the muon. The energy of the muons that arrive intact studied in the last link, has to be corrected for this.
In the same way, if there is an interaction and a particle meets its antiparticle and annihilates into end product particles, the interaction is studied in the center of mass, and any external effects have to be taken into account by going with the correct transformations to the lab inertial system. In particle interactions studied at colliders there are no potential effects to be taken into account. In electron positron and proton antiproton colliders already the laboratory frame is the center of mass of the interaction and no transformations are needed.