Did the Romans eat seaweed?

[Epictetus]

I know that there's anecdotal evidence (at least) of them using seaweed medicinally...

Yes, Pliny's Natural History mentions many of its medicinal uses. See Book 26 Chapter 66, for instance. But he doesn't seem to consider it as a food. Although sometimes he talks about it being ingested, most of its uses appear to be topical.