Yes it is possible to paint over the red wall. With a bit of work. I would recommend using and oil based primer such as Kilz Interior Oil Primer. I don't recommend using a water based primer as bleed through can still occur.
Apply two coats of the primer. A third may possible be needed but I am confident two will work very well. Where you are planing on going with a shaded color it should paint over very well.
If you have a doubt. Then do a small 12"x12" inch patch that is out of eye view in the room. So you can ensure the red will not show through your work. I hope this helps.