This may depend on the type of two-speed motor being considered as outlined by jb.
We have had considerable success in similar applications. In those the motor was configured/wired for high speed operation (in other words all low/high speed switchgear removed, solid connections made for high speed only)and the drive was installed in the supply line ie as would be the case in any standard cage motor application.
Would suggest you consult the motor manufacturer before proceeding.
selecting a high speed config, will allow the machine to regulate it speed on a wide range,,.but it is still depends on the application.
the only thing the machine will face to, is the harmonic content of the VSD output where dual speed machine are not design for VSD control especially the winding insulation.
Comment: The VFD DC-AC inverter output can be engineered and designed to produce a nearly sinusoidal output voltage wave with very small harmonic distortion. Such a VFD may be applied to standard induction motors.
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POWER QUALITY OUTPUT
Multi-level design inherently provides a sinusoidal output
without the use of complex external output filters. There is no degradation to the waveform at lower speeds, unlike inefficient traditional designs, which may be sinusoidal only at 60 Hz.