Will the negative charge on the capacitor be neutralized?
No, there is no circuit being completed, hence no means for the "charge" to flow into the battery.

It appears that you expect a Coulomb static charge behavior to occur, such as in a Van De Graaf generator. That's static electricity, which albeit analogous to battery type "Direct Current" electronics, is not quite the same thing.

For one thing, batteries are not Coulombic charge storage devices: They are, at the simplest, reversible chemical reaction storage of energy resulting from ion flow caused by a potential difference. "No actual electrons are harmed in the battery process".

Also, though capacitors are technically charge storage devices, they would require a discharge path towards a lower absolute static charge potential point, for what you have asked, to occur. That's not the case here.