If we pass current through a gas, like in the discharge tube, the electrons will accelerate in the electric field. The accelerated electrons will collide with gas molecules, and transfer some of their energy to them. Thus, producing gas molecules in the excited state. The excited molecule can come to ground state by emitting its excess of energy in the form of light. Thus, we can see gasses emitting light when current is passed through them.
Will the current carrying solid conductors (example,copper wire) emit light similar to that of gases?
$\large{\color{red}{\checkmark}}$This particular question is about the current carrying conductors which are not insulated (seen in everyday life) and so as to why they don't emit light. If we consider other cases, there will be radiation emitted from the conductor as discussed in this particular question.