Change a quartz clock timebase by changing the frequency of the quartz crystal oscillator?
In principle, yes. If you have a device that uses a crystal oscillator to generate its timebase then you can change the timebase simply by changing the crystal oscillator frequency.

In practice things get more complicated. A given device will only operate over a specific frequency range and you can't violate that limit. Furthermore, if the oscillator circuitry is built in to the device and a simple crystal is connected to it then you have to consider the electrical characteristics of the oscillator circuit. The manufacturer of the device should provide information on selecting a suitable crystal, as well as the associated capacitors.