That is a good point: Could you even understand what the other people were saying even if you could speak "English"? I have heard some modern day people from England whose accents were such that I could barely understand what they were saying. How much worse would that be in King Arthurs time?
You have found the one flaw in the realism of that novel!
On day 1, the Yankee would have only a few useful words in common with the locals; on day 10, the Yankee could hold a simple conversation; day 100, the Yankee would still have an "accent", but communication would bottleneck more often on lack of shared fundamental assumptions, than on lack of shared vocabulary. YMMV, some people learn languages and dialects faster than others.