Not the parent (and gotten my PhD more then 25 years ago), but the answer is no.
Quantum mechanics is a fickly thing. Schrödingers cat has not been observed ;-) because scaling kills the quantum mechanical properties.
My (entirely theoretical) PhD project dealt with a 2 dimensional electromagnetic cavity, with one 'perfect' mirror (100% reflecting) and one 'imperfect', say 99.999999999% reflecting.
My results were that if you started with a 'squeezed' vacuum, in just a few roundtrips, the 'squeeziness' disappears, due to the bath/loss of the non-perfect mirror. My 'gut feeling' tells me that if we have enough qbits to actually factor something more then 2x2, the loss/bath effect will delete any useful use of the quantum computer.
So I am in the 'will not happen' category. (Not in 1, not in 5, not in 30 years, not in 500 years).
This is different from classical error correction: as far as I understand Schors algorithm, there is no 'get N approximate answers, combine them, and get a better answer' part in there. While classically you could do 100 measurements and get a better approximation then with just one.