does SMPP works with wichever SMSC.
Most of the SMSC's support the SMPP protocol on IP Network side, as SMPP is not propreitory to anybody. But some SMSC's developed big cos will support only their protocol. For example, Nokia's SMSC supports CIMD protocol, which is designed by Nokia folks. Some other European based SMSC's support EMI protocol. So, better you contact your SMSC vendor for this.
But to answer strightly your question, "Yes, SMPP works with any SMSC, if that SMSC supports SMPP protocol".