Toe Overlap

So, what you're saying is... When I'm moving along at reasonable speed I will not able to make as sharp movements (without falling) with my bar so that I'll be able to touch the front wheel with my toes?

When moving at a reasonable speed the bars will not be turned enough to cause overlap. It is only at slow speeds where the bars are turned enough to cause the wheel to overlap.

This is not specific to the KHS as pretty much every track/tight road frame has overlap so it should not factor in your choice of KHS but rather whether you want a fixed bike.