I was talking this over with my wife last night, playing devil's advocate and the like and where we got to was; if I just take off the front wheel and pedal, then it's still a bike, still a no-go. But if I can't put it back together using the parts on my back, then it's fine. At this point my wife said "well why would you even want to do that then?" Well I ride a 29+ and my buddy rides a 26fat. we swap front wheels when we disassemble. Then neither of us can physically build a bike with the parts on our back. Wife gets angry and says I'm being pedantic.
It sounds like it really comes down to the opinion of the ranger who sees you, if you even meet one.
And I would doubt any hiker would have issue with you hiking with the bike on your back. At that point you are a hiker too, just with a ridiculous pack.
I guess I don't really have anything to add other than contacting the ranger district before hand until someone says "go for it" then write their name down so when you run into ranger 'bob' you can say ranger 'joe' with your district said I could.