Yes. The Customer is a part of the Value Stream. Talking about Lean-Agile framework, customer is an important entity.  There are TWO types of customers – Internal and External. Internal Customer can be the IT department or the HR systems, requesting to build solutions around their requirements. External customers are the ones who are the direct buyer of the SOLUTION.

Below are the few responsibilities which the Customer has to fulfill (as per ScaledAgileFramework.com)

• Participate as a Business Owner in PI Planning.
• Attend the Solution Demo and possibly System Demos; help evaluate the solution increment 
• Participate in Inspect and Adapt workshops; assist in removing some systemic impediments 
• Interact with analysts and SUBJECT matter experts during specification workshops 
• Collaboratively manage SCOPE, time, and other constraints with Product and Solution Management 
• Help define the Roadmap, Milestones, and Releases
• Communicate the economic logic behind the solution and help validate assumptions in the Economic Framework 
• Review the technical and financial status of the solution 
• Participate in beta testing, User Acceptance Testing (UAT), and other forms of solution validation