With The Improved Transmission Characteristics, Would It Be Necessary To The Gearbox (i.e. To Make It Tougher)?

It's not needed as improving the shift times/pressures will actually increase transmission life (less slippage = less heat/wear).

These tune alterations do electronically what the shift kit does mechanically to a degree.

If you still want to toughen up the transmission further then fitting a shift kit and 2nd gear corvette servo would be the next step.