Since the Ice Climbers don't even have an emblem (but rhythm, brainage, diary, etc exist) I wonder if they even got further than pre-production (before Sakurai joined the Smash for 3DS/Wii U team full time). I don't think it's that far fetched to assume a lot of the groundwork for the game was laid out while Sakurai was finishing Kid Icarus: Uprising.While there is logic behind that, it's just an assumption. No "source" behind it, so to speak.
I am pretty confident that 8 player Smash had nothing to do with the IC getting cut as Sakurai has gone on record as saying the 3DS limitations are what lead to their exclusion. If anything, I think it may have been the opposite of what you are proposing here, with Sakurai deciding to implement 8 player Smash after he realized IC would not work. I don't recall, was 8 player Smash discussed in the design documents?
I don't necessarily think that 8 Player Smash was the sole reason Ice Climbers were cut, but it's going to be the reason why they can't even come back as a Wii U exclusive.