If you take out and eyebrow ring will the hole stay visible?

Yes. Since the diameter of an eyebrow ring is typically larger than the diameter of the holes a piercing usually closes when changing your jewelry, the skin has to rip when removing the jewelry. This leaves behind a more noticeable scar. If the hole stretches due to years of wear, it may become looser but would have to re-stretch if jewelry were to be reinserted.