Can I paint over room borders without removing them?

Yes but tape well at wall and floor.

No remove them, it will show through and eventually have to be removed.

I would use a primer first to cover the colors and prevent bleed through the paint but you might end up seeing lines where the border ends.

I would remove them now to avoid the possibility of then peeling later. Also its easy unpainted and difficult once painted. Get a scoring tool, peel top layer if possible. Score, wet and scrape with plastic putty knife. After fill any dips and scrapes to wall before painting. Hope this helps

Oops..got to thinking about my answer and I read your question wrong. I would try to remove the border as best as possible. You may need to sand some of it but if you score it with the scorer that makes tiny holes then spray with bottle filled with water...it will seep under it...use a putty knife or wall paper remover and it should come off pretty well. Good luck.

When you use the scorer, spray the border down with fabric softener and water. Let sit about 10 minutes. Then use a scraper and the border will come off easily.

Best to remove.Moisture in the primer and paint can make it bubble and peel. Future removal would be a problem.