You can succeed with SN even with vomiting because the dose that's recommended (25g) is overkill. Much smaller amounts (less than 10g) have been known to kill people, so as long as you don't immediately throw up everything right after ingestion, presumably enough SN will pass through your system to be fatal. Theoretically if you then took another dose and threw up again, even more SN would get through, thereby raising your chances of reaching the fatal dosage.
With that said, personally I think the "second cup" recommendation is nonsensical because if you throw up after the first ingestion, chances are you're not going to physically be able to bring yourself to retake the poison that your body just rejected.