I don't think there is a relation. Carrageenan is a polysaccharide. That means it's a long chained sugar type molecule. The long chains get tangled up and that's why it makes a good gel or thickening agent. MSG is the sodium salt of glutamic acid, an amino acid, which is totally different from carrageenan. It's a component of protein, not sugar. There's no way you can make protein from sugar. I don't see how MSG would get into carrageenan, unless there was some protein in the original seaweed from which it is manufactured. Seaweed is not a good source of protein. So there would be an extremely tiny amount of overall protein in the original starting material, and glutamic acid would be an even smaller part of that. Perhaps tiny trace amounts would be in carrageenan used in food, but I doubt it. Even if it was, the amount of carrageenan needed to thicken something is minuscule, so this would dilute the MSG even more. My feeling is that either there is no MSG in it, or if there is, the amount is so small to be nearly undetectable.
On another note, I looked up the major industrial processes for producing carrageenan and they use potassium hydroxide, not sodium hydroxide, as alkali. So you would not have the sodium salt of glutamic acid produced (MSG) if any was produced at all, but the potassium salt, which is not MSG. In addition carrageenan is practically odourless and tasteless. If anything it has a very slight fishy taste. If it had even a tiny amount of MSG in it, you would be able to taste it.
While I know there are a bunch of crackpot websites out there saying there's MSG in carrageenan, a search of Google Scholar turned up not a single scientific paper linking carrageenan with MSG. The only publication that makes this claim is a non-scientific, non peer reviewed book by Russell Blaylock (1997) that describes a made up non-scientific claim that food additives are excitotoxins. This is junk science, not recognized by the scientific community. I would not trust it. There have been no proper experimental studies linking MSG to carrageenan. Everything out there on this subject is based on the untested opinion of one guy who didn't even do any experiments. That's not science.
But the bottom line is: if you find that your body is made uncomfortable in any way by eating things that contain carrageenan (whether it has MSG or not) then you would be advised not to eat these foods.
making a small donation to science.ca.