Generally speaking, yes and no.
IME, the red phase goblins generally remain red, but they do sometimes go a little pink depending on mood. The gray fish you see in the second shot (with the brasiliensis) is a different species (I. japonicus):
<img src="http://i285.photobucket.com/albums/ll73/hixphotobucket/Our%20Fish/goblinout700.jpg">
The ghoul came in as an almost solid gold color (you can see it on its side by its pectoral), but it lives in a pretty purple tank, so it has taken on coralline colors.