What would happen? Headphone out signal from anything going into the Normal "input" on a solid state amp?
Without knowing the exact specifications of the headphone out signal and the input of the amp, I will say nothing "bad" will happen. The input of the amp may overdrive but likely would not bust, and the sound from the amp (especially if it is a guitar amp and not a FRFR system) will make the headphone out signal sound bad.
Solid state is fine. The line level will likely be way too loud and distort the amp output. I still do it on lots of ss amps but turn the line output wayway down. Havent damaged a device yet.
Yep, turn the volume way down on the device you plug into the amp, the signal will be very hot. I did it a lot in the 70's, works fine if you keep the volume level down. If you let it get too loud, it will be very distorted. That shouldn't hurt if doe only briefly, I would worry about it frying a circuit if left that way for long. Turned down so it doesn't distort, no problem.
Hmmm...I wonder what this button does...