Disclaimer: I’m just a user and have no insight into the development process itself.
It’s not an issue with Invoice Ninja itself, so much as the included fonts don’t support the proper Unicode characters. There’s a similar issue with Thai script.
While it should TECHNICALLY be possible to manually install a font and add it to the database, I’ve never been able to get that method to work. Invoice Ninja sees the font and allows me to select it just fine, but PhantomJS (the back-end they use in 4.x.x to create PDF files) just doesn’t seem to want to render the text at all.
As far as I’m aware, they’ve done away with PhantomJS entirely in the 5.0 branch. After a quick test on the demo site, it does appear to render Georgian characters properly in 5.0.13. However as that version is still in beta, I wouldn’t try to migrate over to it just yet.
If you try to edit the database manually, you may have more luck than I did, but just be aware that it always carries the risk of making matters worse. From my personal experience, PhantomJS seems to be the problem in that it just can’t handle Unicode characters other than Chinese or Japanese.