The SMS messages originate from the SIM - the same device that tells the baseband how to connect to the cell network. So it's not possible (ordinarily) to separ

The SMS messages originate from the SIM - the same device that tells the baseband how to connect to the cell network. So it's not possible (ordinarily) to separate proactive SMS from the intended recipient network. However, if we designed an intentionally broken baseband that connected to two SIMs, and swapped the proactive SMS from one to be sent to the other SIM's network, it still wouldn't do much. The SMSes are sent to invalid phone numbers that only make sense to that carrier's internal routing.