Will VFD provide enough startup current for induction motor under full load?
You should be able to find a VFD that will be capable of making the motor produce at least 150% of rated torque at any speed from zero to rated speed. The current required to produce that torque with the VFD should not exceed 150% of rated current by very much. The selected VFD should have a "sensorless vector" or "direct torque control" control strategy. Operating in the V/Hz control mode will probably not be sufficient. Also a VFD that is only rated for fan and centrifugal pump loads will probably not be sufficient. Inquire locally to find a VFD that has a good reputation. There are many manufacturers that have very capable VFD designs>

For more information about how a VFDs can start a motor without supplying high motor current, look at my answer to this question.

Note that you should not use a VFD model for a motor that is smaller than the smallest motor recommended by the manufacturer for that particular model. For the best performance, the VFD must be "tuned" to the motor design parameters. The VFD can do that automatically, but only for the range of motor ratings for which it is designed. The VFD also has built in overload protection for the motor that is limited to a range of motor ratings.