It will be fine. I have a weird daisy-chain of devices hooked up to my monitors so that my personal computer, work computer, and Nintendo switch are all capable of running through my speakers (and monitors).
As far as I understand, “Line” output signals are usually un-amplified, so that is likely better for plugging into an amplifier than a “headphone” output—but honestly, a computer monitor is not a purpose-built audio device, so its likely just a standard 1/8 inch phono jack amplified audio output regardless of labelling, amplified by both the computer running it and the monitor itself.
This is not digital data you’re working with but a literal fluctuation with electrical energy to mimic a sound wave-form so anything with a phono plug is compatible with anything else—it’s pretty simple technology.
The worst case scenario (assuming this stuff is all properly made) is a buzz coming from the amp when no other sound should be heard.
I am also curious about the broken front panel head phone jack and failure of the rear panel audio out.
In the case of the front panel, is it physically damaged so it no longer works or did it just stop working after the computer toppled. If it’s the latter, you may wanna open up the case and see if your front panel connectors on the motherboard came undone (you’ll need to consult your motherboard diagram to find where those are but since you said you built the computer I assume you know that).
As for the rear panel—standard check for driver updates or system sound settings being incorrectly prioritized. I have an asus motherboard that I selected specifically for optical audio output because I didn’t want electrical interference from a simple phono plug (and I was being precious at the time) but the optical output will occasionally stop working and I’ve never been able to fix the issue—likely just a software glitch because a restart usually fixes the issue. I now have my Klipsch powered speakers connected both via optical out and USB as a backup, which brings me to my final piece of advice:
If all else fails, just get a USB Digital Audio Converter and use that as your system sound output if you want to continue using your amp and speaker setup, OR, just get a pair of actual computer speakers with USB connection—dealer’s choice.
Glad it worked! Happy computering.