Many plant troubles boil down to one of two things - too much water or too little light. I'm guessing your situation is a bit of both. Don't water on a schedule. Water when the plant needs it. Until you learn to read your pant's behaviour you'll need to feel the soil at a little depth. And get it into more light.

Definitely beef up the light. "Bright light but not by a window" generally does not equal bright light from a plant's perspective even if it seems bright to you eyes.

Do you think it will "come back" or is it too far gone?

It will come back. Swedish Ivy is like wandering jews. They become unattractive 3 or more times a year and are just in need of being cut back nice and hard. It will grow back lusher and fuller than it was before. That said, the plant must be in decent light from an east or west window or very near a north window. The leaves of this plant get a bit dull looking when it's time to water. In summer, the plant wants water because it is actively growing and needs more water, in winter when it's barely growing or growing less, the same water you give in summer will kill the plant, because it cannot use it up as it could when growing more. You really do have to watch the plant to let it tell you how long you can go between waterings. So, you picked a good plant to experiment on, as these will regrow pretty quickly. Good luck.

Does this pot have a drain hole in the bottom?