First thing, does it show up on any other device? If it isn't showing up on any other devices, then your hotspot isn't broadcasting a signal. Otherwise, it could be broadcasting a signal but your HP might be getting cross talk, is too far away, has one of it's antenna's disconnect, etc.
There's a potential that it will. "Potential" It could be ok, but any time there's a burn mark on any sort of adapter, charger, plug-in, you're only asking for trouble in the long run. If it's as easy to replace as that is, replace it.