Well, like many musician's, I'm broke. I know you should use a PA system, but can an amp work as a ghetto rig? The imput jack is the same size, so I couldn't see why not (assuming you set the tones and effects to a decent place).

Overall, could I plug a microphone into a small guitar amp and get it to sound ok?
"This nightmare's gonna break me.
Please, Daylight, save me..."
That's what I do with my band, you just have to mess with the equalization to fit your voice, and be aware that because it's meant for guitar, it'll pick up every tiny little thing you do, if your k's and T's are too pronounced, for instance. But other than that, yeah it works fine.
It'll work and not damage the amp. However it will sound like crap due to the electronics of a guitar amp and how it's designed to interpret a certain type of signal.

Better amp choices for vocals are keyboard, bass and acoustic amps. If you check out some second hand listings you may be able to score a practice PA for cheap.
And no, Guitar Hero will not help. Even on expert. Really.
I would say no, but I guess it depends on your definition of 'ok'. Back when I was a struggling young artist in highschool, we used my friend's Laney tube amp (40 watt-ish, I think?), and it worked, I guess, but we always had issues with the volume. We were using in a band-setting (guitarist, drummer, and and vox), and you could barely hear it, singer was always straining himself to be heard.

So I certainly wouldn't recommend it, and unless you have a very big amp, it's not going to work very well, but it can be done.
It'll probably sound like crap, but strapped for cash generally means that any kind of music you're making is going to sound crappy. (Not about writing, but cheap gear all sounds bad. Some things just sound slightly less bad.)
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get a cheap mixer, then output it to multiple amps. example:

Mic>Mixer>output to two amps (left and right pointed outward like a PA)> then output to another amp but face it toward the singer (infront of him) to use as a monitor.

It works for my band with all the cheap solid states and practice amps we have lying around. Our mixer was only like $70. Behringer makes cheaper ones. Using a mixer you can have multiple inputs (so you can have backing vox) and multiple outputs.

Hope I helped ya!
Guitars: Epiphone Slash AFD Les Paul, Schecter Omen-6, and Fender CD-60 Acoustic
Amp: Jet City JCA20H with JCA12s cab
Pedalboard: Crybaby Classic, Boss DS-1, Korg Multi FX, BBE Boosta Grande, Rocktron HUSH Pedal. ProCo Rat.