I noticed no-one answered your question.
Yes, you can change the speed at which vari-audio follows the pitch. Although it’s not really like that, what you do is change the steepness of the corrected curve…
In fact this is one of the features of Vari-audio which is better than Melodyne because you can actually edit the final pitch curve with a greater degree of control.
So, to edit the pitch curve, first set to Pitch&Warp, then hover your mouse over the top of the chunk, you will see a dark thick line across the top of the chunk, and somewhere along it you will see a single thin vertical which divides the chunk into two. This vertical line is like the fulcrum, and when you adjust the curve then the part of the curve at that line doesn’t move. So, just click while hovering to change the vertical line position. Then, to adjust the curve, hover over the top left or top right of the chunk until the cursor changes to up/down arrows, then left click and drag up or down. The curve will move, and you will also see the orig pitch curve for reference. In this way you can change the curve steepness, change the fulcrum position many times over and adjust the pitch curve specifically how you’d like it. I quite often use this method to create a believable slide into and out of a note which I’ve ‘straightened’ to hell.