I would say that GBR are a little more sensitive than the average fish, but I wouldn't necessarily say they just "die for no reason". Mine have, for the most part, been healthy if I can get them past the acclimation stage, even in my water which is certainly less than idea for them (high ph, high kh). I've mostly kept golds and electric blues, not the standard gb, but they're the same fish, just different color morphs so shouldn't matter. 6 is a lot for a 20L though. I had 6 in a 46 bow, and while it worked, there was a little more aggression than I cared for and I ended up moving 2 out to another tank to give them more space. And those were young, unpaired fish. They are fine with the other tank mates though - angels, betta, guppies, cories, plecos, swords, diamond tetras, etc.
There's also a very strong likelihood that they will take out your cherry shrimp population. Mine even went after the smaller amanos.