Laser tube need a certain pre-ionization time when it starts working, is it possible to speed up the pre-ionization time by intentionally sending a modulating signal?

No, it cannot, unless by modifying the program. The pre-ionization of the laser tube is done by the internal pre-ionization circuit. The pre-ionization circuitry starts to work as soon as the laser tube is switch on.  An artificial modulation signal cannot help the laser tube to complete the pre-ionization state.