As I see it, there's the Grail-Arthurian-Fisher King vortex (which has proved capable of aceepting anything modern Romamtics care to toss in), and then there's the carol.

Both involve a castle (or a "hall"), Jesus, and striking, perhaps intriguing Christian images - differing images at that.

Other than that, I think any "connection" (which often means that one was inspired by the other, or that they share a common origin) remains fanciful.

("What if," "maybe," and "I don't see why not" are popular Mudcat arguments, but they are not evidence.)

Now if the carol actually mentioned a Grail, or a Percival, or a Fisher King, or even an Arthur, the situation would be very different.
But it doesn't.

If there's any connection at all (and why should there be?), it could be that the person who made the carol was familiar with the internationally popular Grail story. But maybe not. It can't be shown from the texts, and if the Grail had ever been of importance to the song, it's hard to understand why it would have dropped out.

If the carol-maker was a visionary sort, he could have made the whole thing up from his own imagination, no further explanation required. Possibly the weirdness of the words helped keep the song from being more popular in tradition.

As is so often the case, there's no way to know any of this.