If someone starts singing a song a cappella, then is it necessary for this person to sing in one of the 12 Western keys (A, A#, B, C, C#, D, D#, E, F, F#, G, G#)? For example, would it be inappropriate for him to sing between 2 keys? What if a guitar is playing along and he is singing between 2 keys--should the guitar go down/up to match the singer's intonation, or should the singer change pitch to match the intonation of the guitar?
Certainly, if a song is sung a cappella there's no guarantee the pitch won't be 'in the crack' between keys based on A=440 (or any other consistent scheme). There's also no guarantee the same pitch will be maintained throughout the song. That's one reason that 'just singing' a song into a recorder then sending it to a musician to have a track built round it is a bad idea. (Another reason is that the timing is equally unlikely to be consistent.)