No. But before I talk about the production of The Little Drummer Boy I should address I think the original story about Schulz has been exaggerated.

The concrete evidence we have for the "religion issue" comes from the 2001 ABC special The Making of 'A Charlie Brown Christmas' which includes an interview with animator Bill Melendez. ("Sparky" is Schulz. Lee was the other producer.)

I told Sparky at the time, and I think Lee did, too, it's very dangerous for us to start talking about religion now. And I remember he [Schulz] turned to me with his strange blue eyes, and he said, 'Bill, if we don't do it, who will?' So I said, you know, I'll go with that.

Notice that

a.) He only "thinks" there was a producer involved, it may have been only the two in conversation, and the conversation plays out as just a personal conversation.

b.) The resolution was quite fast.

(ADD: Lee also has confirmed the conversation from his end, as per the comments, see here.)

This seems to have been mythologically tied together with concerns from CBS that the show's pacing was too slow (while spending a long time reciting a biblical passage might be considered part of that, it is not equivalent).

I'm also not sure if the "dangerous" quote is really all that accurate for mid-60s TV. One of the most popular cartoons at the time, using claymation by Clokey (of Gumby fame), was Davey and Goliath (about a boy, Davey, his dog, Goliath, and how they can overcome trouble by believing in God), with production starting in 1958 and the first episode showing in 1960. It was produced first by the United Lutheran Church in America and later the Lutheran Church in America and it was indeed fairly explicit with its religion, with A Mighty Fortress is Our God as the theme song.

In the time period where you are thinking between the Charlie Brown special and Little Drummer Boy, they had an Easter special where Davey and Sally visit their grandmother who bakes a Happy Easter Cake. However, she dies before Easter comes, making everyone sad, and the finale has an angel talk to Davey, Sally, and the dog Goliath about how she's in Heaven and they'll get to see her again.

Davey and Goliath was wildly successful with an estimated "tens of millions" of children and was generally considered the gold standard for religious children's television. Really, it was Davey and Goliath's success that made religious children's television more acceptable.

For Romeo Muller, who had previously wrote the Rudolph special, the script for Little Drummer Boy was apparently his favorite. Quoting the historian Rick Goldschmidt:

Arthur Rankin called Romeo one morning and informed him that he had told NBC about a Romeo Muller story that would be delivered that afternoon. In one hour, the clean, simple story, which Muller thought was the best Christmas show he had ever done, came to him. He typed it up and dictated it over the phone to Arthur's secretary and Arthur rushed it to NBC that evening and sold the show.

This does not sound like a troubled pitch or production. Note that animating was done through the Animagic method (stop motion using puppets as opposed to clay, the actual animation was done in Japan) and there was a year-and-a-half process, so the actual script would have been around '66, the year the Easter Special I mentioned showed. This means it is possible Muller had the Charlie Brown special in the back of his head, but it was the presence of Davey and Goliath that allowed for unabashed religiosity.

...

Clokey, Joan. Clokey, Joe. (2017) Gumby Imagined: The Story of Art Clokey and his Creations. (2017). Dynamite Entertainment.

Werts, D. (2006). Christmas on Television. United Kingdom: Praeger Publishers.