Would then base react with water?
Your proton-charged water will not last long enough to react selectivy with any electropositive metal or a base that you add.  Electrostatic forces are powerful.  The excess protons will grab electrons, generating ions that themselves grab other electrons, until eventually the beta particle electrons that were emitted to begin with get consumed to rebalance the charges.  You might get some unpredicted chemical reactions but no lingering excess charge.