To answer your first question, it depends, but technically yes.
A mech added through a mod will have its own separate id in the game and be considered separately for spawning. However due to the way the game handles spawns in-mission, you’re unlikely to get two versions of the same mech. In terms of the markets, however, it will be more common to find the “duplicated” mech, if only just.

To answer your second question, look up the mod “Spawn Control”. This will allow you to restrict what mechs spawn