Yes, although starting sensorless brushless motors under load is one of the hardest aspects of operation of sensorless brushless motors.
The key to successfully driving brushless motors (and stepper motors for that matter) in an energy efficient and practical way is the timing of the power input into the motor coils. If the timing is slightly out then this will slow the motor down and also create excess heat and lost energy. When a motor is up and running it is relatively easy to know the rotor positions on a sensorless brushless DC motor as this can be detected using back EMF and then optimised at the testing and setup stage by through testing and understanding the exact motor being used.
However, at the startup stage it is impossible to know the rotor position on a sensorless BLDC motor because there is no movement from which to gain information. It is therefore quite common for sensorless motors to jump around a little at the start if they have not been properly optimised because the controller being used is powering on coils on assumed position and then hoping to pull the rotor into that pattern when it will therefore function well.