I’m now trying to envision Number One instead of Spock throughout all the TOS episodes. Would Pike and NO have become friends like Kirk and Spock? Could it have been a Pike/NO/Boyce triad?
Very probably not. For one thing, gender attitudes of the era would've precluded it; Number One's relationship with Pike would've been Unresolved Sexual Tension like Kirk/Rand. A close platonic friendship between a man and a woman just wasn't something you were likely to see.
For another, the Kirk-Spock friendship happened because Nimoy's breakout popularity threatened to overshadow Shatner as the lead, so Isaac Asimov suggested to Roddenberry that he make Kirk and Spock an inseparable duo. All due respect to Majel Barrett, but I doubt she would've had the charisma to be as big a breakout star as Nimoy was. At least, not in a role as stoic as Number One, as opposed to her bravura turn as Lwaxana decades later.
Impossible to answer, but the Shatner/Nimoy/Kelley chemistry wouldn’t have been easy to replicate. If Spock had remained a second tier character he might never have become a breakout one as he did the way things actually played out.
Now that you mention it, I think the same thing probably would've happened, with Nimoy's charisma making Spock the breakout character. Really, if you look at early season 1, Spock is a "second-tier" character in a lot of it, tending to get left behind on the ship while Kirk carries the main story. He was given more to do as the series went on
because of the appeal Nimoy brought to the role.
Just think of Worf, who started out as a literal afterthought, a character who wasn't even in the original TNG series bible and was just tacked on to be the token Klingon. But thanks to the richness of the character and Michael Dorn's performance, he grew into one of the most important and prominent characters in the franchise.
In the beginning Kirk was largely a rename of the Pike character, but it’s Shatner’s performance that made him and the character distinct. Even if Hunter had stayed and grown into the role it’s hard to imagine him being like Shatner’s Kirk. No, he wouldn’t have been—he would have been something else. Maybe more like first season Picard?
To an extent, probably. But it's worth keeping in mind that another factor in "The Cage" was that Pike was at his lowest point in the story. Like Sisko in "Emissary," he'd become disillusioned with his career and got his groove back thanks to what he went through in the story. So Pike might've been written differently afterward, and Hunter might have risen to the occasion. I doubt he would've been as effective as Shatner, but you never know.
I don’t know the actor’s ages, but John Hoyt’s Boyce comes across as older than DeFeorest Kelley’s McCoy. Hoyt really seems more the “old country doctor.” And that didn’t change much if at all with Piper. Never mind Pike it’s Boyce who seems more the one who would likely be thinking about soon retiring at least from ship board duty.
Hoyt was 15 years older than Kelley. He was 59 when "The Cage" was filmed.