Oh yes, it is possible: you can spin yarn from seaweed!
A year ago at Wonderwool (I will miss it this year, sadly) I bought few bags of fibre I hadn't yet worked with. Among these were 50g of seacell/seaweed that I didn't finish spinning up until recently. Only took me about a year, but hey! I used the tiny African bead supported spindle I also bought there from Mandacrafts, which spins beautifully, by the way, but it may not have been the greatest choice for this kind of fibre. I think I would have been much faster and better on the wheel instead. Live and learn.
Seaweed top is very slick and shiny, much like silk. It was hard for me to get into the flow while spinning it because of this slickness, actually. After about half was done, I decided to try spinning from the fold for the first time and, lo and behold, that did the trick! I still got stuck fairly regularly, but on the whole this was the best method for the material.
The yarn is very fine and I intend to leave it as a single in order to ply it with other yarn at some point. Right now I have no idea about the yardage, but I expect there's lots of it.
Okay, so should I start on the milk protein fibre next or continue with the baby camel and silk sliver instead? Decisions, decisions.