Big Hero Six was completely redesigned by Disney. The characters don't seem to resemble the Marvel Universe versions at all. They also have had no interaction with the Marvel Universe on film or TV, existing in a world completely separate from Captain America, Spider-Man and so forth.
Lastly, neither the Disney version nor the original Marvel interpretation of the team has had any major appearances in the publishing side of Marvel Comics since the film debuted. If Disney went their own way with the property, I don't think it would improve the popularity of the O.G. versions of the Royal Family. (If anything they would be forgotten and replaced in people's minds by some kid friendly goofball "toons." Much like how Steve Gerber's Howard the Duck comic is completely overshadowed by the terrible George Lucas film version in our collective memory. )