Not necessarily, there are industrial dyes which will stain PVC pipe very vibrant colors, but I've not seen it used on styrene before.
I don't see why a very strong dye wouldn't work, but you're not going to get a very good ivory color out of it without a tremendous amount of trial and error... and even then you may not get a consistent tint.
You can do things to age it but your limited to the wind basically when it comes to control of the process. Leave it in the sun, spray it with WD40, its already been mentioned about tea and/or coffee, CA glue spray kicker will yellow it, crafts type powder tints if fine enough will stain the surface. Of course were talking 3000 and above mesh fine but this is my styrene work surface from the past week. Think I may frame it and hang it on the wall now I look at it.