If I'm understanding your post correctly (it's a bit confusing with A/C meaning both Air Conditioner and Alternating Current), then yes, it could.
The loose connection has a higher resistance, and gets hot. Assuming it's a bad connection at the distribution panel, the heat gets conducted via the neutral bus bar to all the other connections, making them hot (but not as hot as the one for the air conditioner). Fun times ensue.
I would probably replace the bus bar and strive to reconnect the wires back where they are not obviously heat damaged. It may be hard to get sufficient slack in the wires. Bus bars are neither very expensive nor difficult to find at electrical supply houses.