I think that we’d still need the Church.
There is evidence enough that even with KJV as the ‘standard’, there are so many thousands of interpretations and understandings, that its ineffectiveness as a Sola is very apparent.
KJV is based on Textus Receptus which is as bogus as a three-dollar bill. It's appeal comes from the fact that the Protestants had a hay day altering an already altered and thoroughly corrupt text.