Yeah a burnout could cause problems with your abs and braking systems. You're using the brake to try and hold back all that pressure, and spinning your wheels while holding down the pedal can be real hard on your pads, discs and drums also.

 

When you replace the front abs harness, left and right, or just the faulty one. Be sure that you pinch the connectors a bit. Before plugging in the new harness. The two prongs on the new harness seem to be a bit narrower than the original. By pinching the female connectors, you ensure a good contact, when plugging back in. Otherwise, the abs and brake light will stay on. Good luck