Can initial Sales Order get authorized by 3rd Party web order, but do settlements in SAP with iPayment?

Yes - when Sales Orders are authorized with a 3rd Party Web Order Program, you can import the Documents with the Authorization Token into SAP B1, and this allows you to do the settlements in SAP B1. You also have the option to store the CC Token on the BP Master data for future transactions. 

See attached B1 iPayment integration document

• B1 iPayment integration - One-time credit card.pdf600 KB