Can ascorbic acid be neutralized and keep it's elastic properties in dough?
There is high probability the desired properties of ascorbic acid are directly related to acid being acidic and in the free acid form, i.e. not in the form of the ascorbate.

It is hard to advise, not being familiar with this part of the applied food chemistry, it the effect of ascorbic acid happens in the cold dough conditioning stage and/or in the stage of the later thermal processing, in case of noodles.

If the sodium carbonate is added later to the dough, it is unclear, how well would be the dough mixed to neutralized the acid, and what the sideeffect would be.

Bakerpedia.com  explicitly advices against using ascorbic salts.

I highly advice to experiment, as theory will probably not provide clear advice.
I am not sure, if the acid is applicable to the noodle dough as much as for bread dough.