I would not as the "Customer" is the recipient of the "Process"
The way the SIPOC is built is that is -
Suppliers to the process : Contributors or who provide input to the process
Inputs provided by the supplier : What are the inputs provided to the process ?
Process : Where does it start and where does it end ?
Output of the process : What are the services or products offered to customers ?
Customers of the process : They are the consumders of this Process and often specifying their requirement.
The way the SIPOC is built is that is -
Suppliers to the process : Contributors or who provide input to the process
Inputs provided by the supplier : What are the inputs provided to the process ?
Process : Where does it start and where does it end ?
Output of the process : What are the services or products offered to customers ?
Customers of the process : They are the consumders of this Process and often specifying their requirement.