From listening to tracks on the boxset's website and discussions here and there, the answer would seem to be "not really, but it wasn't completely possible anyway".
When I say "Perfect", I mean it really specifically, and I'll explain that in detail for each song.
Here are the songs on the boxset that appear on their album segued:
White Queen (Father to Son at beginning)
Tenement Funster (Flick at end)
Flick of the Wrist (Tenement at beginning, Lily at end)
Lily of the Valley (Flick at beginning)
Tie Your Mother Down (A Day at the Races album intro at beginning)
TYMD is easy -- a Perfect unsegued single has been available from day one, on Greatest Hits compilations, etc. I honestly didn't listen to this on the website, but I'm including it here for completion's sake.
Tenement Funster is a bit rare. A Perfect unsegued single appeared on the vinyl of Queen's First EP, but they botched the UK 3" CD single and just faded out the album track (meaning you can hear piano from Flick). The Japanese 3" CD single restored the correct version. On the website it sounds like you get the botched "fade out" version (which therefore isn't true to the original vinyl).
Flick of the Wrist is rarer than TF and may not exist. Being the middle of a 3-song segue makes it easier to mess up, and unfortunately the most common versions are not quite Perfect. Like Tenement Funster, an album fade was used on the UK 3" CD single (Killer Queen instead of First EP this time) instead of the original vinyl (and Japanese 3" CD single). Even the original vinyl wasn't quite perfect as it starts on the second set of piano bits a few steps down. There's supposedly a Dutch Killer Queen with a Flick that starts on the correct notes but I've never heard it and I'd be fascinated if it had been shared previously. From the site it sounds like you get the not-quite-perfect (but better than the Tenement botch) UK vinyl / Japanese CD single version.
Lily of the Valley is so rare it probably doesn't exist. It shares a similar problem with Flick because the most common versions are missing the first set of piano bits (this time in the same key and essentially the same rhythm). The original UK single starts with the second set of piano bits, and this is what the site sounds like. There was a US re-issue that is arguably a botched edit as it includes the last bit of guitar from Flick. So here I say "probably doesn't exist" because there might be an acetate or something out there I'm unaware of.
White Queen again probably doesn't exist, but only because I'm being really, really specific. The Queen's First EP version (all editions this time) simply fades into this once the Father to Son business is over. This is what it sounds like on the site too. Again, "probably doesn't exist" is trying to cover stuff outside my knowledge.
So with the 3 that were definitely commercially released, they screwed up 1, and while they were true to the UK Killer Queen vinyl it would have been really cool to release something really rare in the Dutch vinyl version (again if it actually exists I want to hear it please please please).
With the 2 that weren't, they stayed true to the original vinyl, and it would have required going back to the Masters (if they exist) to generate something purely for completion's sake.
I guess my feeling is that if Greg were allowed to pursue his in-depth version, we might have got all 5 perfect.
With the current product, we get one kinda-rare, near-perfect unsegued single in Flick of the Wrist.
For my money, that's not worth the whole set, but if they could sell the individual tracks in the US, I'd at least buy Flick.
If I'm missing something please let me know.