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Shouldn't. The SES light is for the powertrain, the ABS INOP light is for the ABS. I just had an ABS failure last week, and only got an INOP light, no SES light.
I just took a quick look though all the PCM codes in my tuner software and Sam is right, there is no SES light code for the ABS, so it must have been my ABS INOP light.
There are SES codes for theft deterent system not working properly and the traction control not working right just for reference. I found a code #1659 that just says "Refer to Service manual", that's a helpful code right there.

There is also a code that is supposed to light up your MIL light when the MIL lamp doesn't work.