You can if you sand the daylights out of it, but that will cause a "bowl" effect.
I have oak butcher block countertops. There was a stain that I just could not get out, so I lightly sanded the area. I got some small jars of acrylic paint from the craft store in wood tones. I painted over the stain and when that dried, I brush stroked a fake grain. When that dried, I gave it a light quick coat of sealant and then heavier coats after that. You cannot even tell.
Another time, there was an accidental discharge of a firearm (don't ask) that hit the oak floor on an angle and chipped out an area as big as a big fat thumb. I filled it with wood filler and followed the above steps and you can't even tell where the bullet hole in the floor was repaired.
If you are not handy in mixing paints or with this type of detailed work, ask a friend to help you.