Well, by and large 'accelerating an atom' means accelerating the nucleus. Since it's tens of thousands of times heaver than the electrons. The motion of the electrons and the nucleus is largely decoupled (Born-Oppenheimer approximation, Franck-Condon principle) due to this large difference in sizes and relative velocities. A popular analogy is to flies buzzing around an elephant. The elephant moves so much more slowly than them, that they hardly change their motion at all to compensate for it.
So in general, you won't see emissions from an atom when another atom collides (e.g. two helium atoms) because the relative velocities of the nucleus and electrons does not change enough, fast enough, to cause electronic excitations. Remember, the electrons in an atom are moving at almost relativistic speeds. If you're talking about a polyatomic molecule, however, accelerating a single atom is just a vibrational excitation of sorts, which means some or all the kinetic energy can be re-emitted as radiation (selection rules apply, your results may vary).
Given that the atom/molecule is neutral, you can't accelerate it with a field. (ignoring possible but largely negligible effects like using a magnetic field to accelerate a paramagnetic molecule) The only way this can occur is to slam another atom/molecule into it, in which case you may be able to get thermal radiation, especially if the molecule has some dipole moment.