A VFD, when _properly configured_, will permit full torque operation at low speed. The requirement for full torque is that the magnetic field be developed to full flux density.
The motor may not be capable of continuous operation at 100% torque and low speed without overheating, because cooling will be reduced, but it should be able to produce full torque.
One significant issue is the proper drive voltage at low speed. To a very good approximation, the proper voltage to achieve full saturation is proportional to the drive frequency. This is such a good approximation that some drives simply use 'constant V/Hz'. However this approximation ignores the resistance of the winding, and falls apart at low speed.
When you want to operate a motor at low speed, the proper drive voltage to achieve full saturation is greater than that predicted by 'constant V/Hz', and a drive using constant V/Hz control would end up with insufficient magnetic flux and thus reduced torque capability. I believe that even the simplest 'constant V/Hz' drives have a 'low voltage boost' setting that helps compensate for this.