Or maybe that mission never happens and as soon as the Narada exits the black hole Data's head disappears from the cave.
Not possible, since the prime timeline still exists even after the Narada
goes back. It creates an alternate timeline which branches off from that point, and which does not overwrite the existing one.
And since it is highly unlikely there will ever be an alternate Data (due to the butterfly effect), then in the Abrams timeline, nobody will ever know whose head that is.