Great question. I tested this using a red waxed thread for a different project that you can see in this post: iPad Pro 9.7 Inch Sleeve Prototype
The thread picks up some of the char and it really depends on the ounce of the leather and your power/speed settings. The thicker the leather, the more time and power it takes to cut (also more passes), which leaves more charring. It also depends on how you’re stitching (i.e. does your thread move around much as it passes through? If so, there may be more char on the thread. This is a minor note that has relatively little impact).
I’ll also be testing another method of making soon to avoid the char getting onto the thread. Hope this helps!