So, "Encounter at Farpoint," one episode or two? It was originally aired with both parts fused into one.
If what you're asking is: "Is there any footage from "The Cage" that wasn't recycled into "The Menagerie"?" The latest version of "The Cage" is a restored version that combines footage that was recycled into "The Menagerie" in 1966 with re-discovered footage from the original cut of "The Cage". You can tell the difference between the video and audio quality and when one switches to the other. But, there's also a version that's un-restored that mixes Color footage with B&W Footage. The B&W Footage is from the rediscovered Original Negative of "The Cage". Anything that's B&W in that version is the footage that didn't make it into "The Menagerie". (The restored version I mentioned in the previous paragraph colorizes said B&W footage) I haven't been a regular in the TOS Forum for about 15 years, but I thought you were a regular in there? Though I don't know for sure, so I might be wrong. But there has to be a thread about it somewhere in there.
To me The Cage is an episode and something like Encounter at Far Point is an episode, yet something like The Best of Both Worlds is two (for reasons I that hope are obvious even if a person doesn’t agree with me). Still, if it’s 801 or 796 or 800 or frankly whatever then it’s all good. More Trek.
I love that this franchise has reached a level of complexity where answering the question "how many Star Trek episodes are there?" is legitimately more art than science. Not to mention how both halves of "The Killing Game" originally aired in a consecutive two-hour block, but there never was a continuous two-hour edit -- premiere night for those was "To Be Continued..." and end credits, straight into "Previously On Star Trek: Voyager..." I will go to my grave insisting that "Dark Frontier" and "Flesh And Blood" are one ep apiece, and "The Killing Game" is two! Though that math gets me Disco "There Is A Tide..." as ep #800. "We'll Always Have Tom Paris" is definitely a more worthy holder of the Notable Episode crown.