Hi,
I had trouble viewing the image, but in general inductance does not affect the turn on of a transistor because the turn on period itself is mostly of high harmonic content and one simple view of an inductor is that is acts like an open circuit for high frequencies.
As you probably know, when you first apply a voltage across an inductor, nothing much happens. With no resistance the slope depends on the inductance, but the absolute current level depends on time. So over short time periods there is very little current change regardless of the size of the inductance. With a small resistance the slope is even less, so takes a little more time to build up the current.
So with a smaller inductor the current slope is steeper, but the initial current change is still zero over a zero time length. So with any size inductor the transistor is still turning on with the same current level. What happens after that though does depend on the inductor size.