You shouldn’t need a preamp after your mic, but you will most likely need an impedance matcher if your mic is not already a high impedance (Hi-Z) mic. If the mic has a 1/4″ plug on it then it is most likely already Hi-Z, so you don’t need an adapter. If your mic takes a cannon (XLR, “three prong”, Lo-Z) cable, then it is most likely Lo-Z. Some mics are internally switchable. But if your mic is Lo-z, then you will most likely need an impedancing matching adapter. They just have a female Lo-z on one end and a 1/4″ plug on the other.

I don’t know about this. I don’t have one, so I haven’t had the chance to experiment with it. Still, this would be a volume / signal level issue, not an “acoustics” issue.

This MIGHT be a solution for guitar, but be very careful applying this to a mic. You’re more likely to get feedback if the levels aren’t just right. I would definitely try it without first. If it turns out you are having problems with the signal, then you can just put a compressor between the mic and the pedal and use that to boost the signal as much as you need. You shouldn’t need a preamp before the compressor. Most comressors already have plenty of boost built into them.

Here’s a video of someone running their voice through it.

It will be fine with voice!
It works with anything. I even used a cymbal with the superego+ and it worked great.
What mic are you planning on using?
Some mics may need phantom power and in that case a mic preamp would have that that option.
Some thing like a Sure SM57 with a transformer adapter would work fine.

What mic is it?

You are best to write Korg and get specs. I have no idea what they use or if its a condenser mic?