This is an unpopular opinion, but realistically, if it had gone down the way it was going down, it wouldn't have made any difference. And a big reason is due to a technical matter.
Listen to the official version of Smile that finally came out in 2011. It clocks in at just a few seconds under 48:00, without "You're Welcome". With "You're Welcome", it clocks in at just over 49:00.
That almost never happened back then with rock and roll stars, especially in the U.S., escpecially in America. And the big reason that groups didn't record albums that long back then is that there's a limit of just about 24:00 per side on a vinyl LP album. What would be "Side B" on the 2011 official Smile version actually clocks in at 24:15 even without "You're Welcome"--just a shade too long.
Now, by 1967, you could squeeze a few more minutes per side on an album, but the only way to do that is to compress the signal, which for the most part means you're going to lose the very high end and top end of the sound. In other words, it means you have to chop out the very low end of the bass. And what did Brian Wilson play? The bass.
The only rocker who had ever recorded an album with 24+ minute sides was Bob Dylan, but that was largely because he had come from the folk music scene where it was common to record 24+ minute albums in the U.S., since there was little bass anyway on an acoustic guitar-and-vocals album. So Dylan had done 24+ minute sides to albums before he went electric, and after he went electric, he kept on doing it.
The Beach Boys on the other hand, never recorded long albums. Pet Sounds was their longest album to date and I think it's about 33 minutes. They may have had only one more album that was 30+ minutes at that point, tops. Most of their albums were around 24 minutes total, with about 12 minutes of music per side, often with lots of filler.
Anyway, this is just a long way of saying that the running order that the 2011 Smile album is presented in, it would never have happened that way. It would not have been released as a 48-minute album, because one side is too long and Brian Wilson would not have wanted to sacrifice the sound of the bass to do it.
So, they would have had cut the album down by at least one song, maybe two. And if it was going to be presented more like a normal Capitol Records release, it would have been cut down to about a 35:00 album.
If they didn't do that, then they would have had to do what Brian Wilson wanted to do, which is to continue to write and record more material. That way, they could release it as a double album, on two LPs. All they needed was about 55-60 minutes of music, more if they wanted, and they were already up to 48 minutes.
That's the reality behind it. It's nice to think they would have released this 48 minute album like this, but even in the best case scenario, the Beach Boys never would have actually considered it in the end, and would have either released a ~42 minute album or a ~60+ minute double album.
If they'd gone for the double album, then forget it. There's no way it would ever have been finished before Sgt. Pepper. At the rate they were going, they would have completed it by the end of the summer of thereabouts, and had it out some time that fall. But by then, in the shadow of Sgt. Pepper, there was an anti-psychedelic trend in the press. The Rolling Stones' Their Satanic Majesties Request got really bad reviews that winter, and albums by groups like Jefferson Airplane and Country Joe & The Fish's that came out that fall and winter got pretty tepid reviews.
Now, if they had released it as a single album, they realistically could have had it out before Sgt. Pepper. But what would that album actually have ended up like? It's nice to dream it would have been like the Smile we've all come to know, but realistically, it would have been chopped by Brian Wilson into something much shorter than what we know simply because of the technical limitations of vinyl records back then (and also Capitol Records liked to get their money's worth per song), and what songs on it do you take off of it? Probably at least a few of the short link tracks, and just leave the longer tracks, which takes one of the most interesting aspects away from the album that make its proponents like it so much.
In the end, I really don't think it would have been met with anything much more than how Smiley Smile was met when it came out at the end of 1967. Because an early 1967 Smile, before Sgt. Pepper would have been a shell of the Smile we all know today, given the way that Wilson would have wanted t master it and how Capitol would have accepted it. For it to come out in the more interesting way that it did, it would have ended up being a double album, released post-Sgt. Pepper, when it may have been met with the same backlash that Their Satanic Majesties Request was met with during that same period. The music press had started to call these bloated psychedelic albums "overindulgent" and then Bob Dylan released John Wesley Harding in December and the press got on the country-rock bandwagon.
Now if it had actually come out the way it is presented on the 2011 Smile album and it actually did come out that way before Sgt. Pepper? Sure, in that unrealistic hypothetical, it may have been received very well and changed everything. But then again, if we're talking unrealistic hypotheticals, it's also possible the Beatles may have released Super Sgt. Pepper instead of Sgt. Pepper which could have been as good as Sgt. Pepper, Ziggy Stardust, The Jackson 5, and the Super Bowl combined, and Smile might have been left in the dust.