You will have some customer contact because that is a necessary part of the job.
Sometimes customers might have a lot of contact up front but then you might go off and work for a while before you ever get back to them. Some customers want constant give and take.
But there are differences between a business analyst and a systems analyst. BAs are usually attached to a group called "Product" or something similar. BAs and Product folks in general communicate with the customers a great deal.
In contrast SAs are seen with larger projects, insuring that subsystems work properly together. They might also work with systems engineers in larger projects. Since SAs are at a higher level, insuring pieces fit together, any issues found at this level need to be worked out directly with the stakeholders. BAs many times do not have the technical skills required by the SA's job.
As a system analyst you may or may not have direct contact with the end customer depending on the company you work for and how the company is organized. Your customer may be the sales people, the marketing team who request specific things in the product and/or the service to meet the end customer. You may even talk or meet the end customer at conferences, trade shows or conventions.
In other words: the number of times you need to interact with the customer depends on who the customer is. It is internal customers like sales, marketing or others interactions will be more often than the actual end customer which may or may not happen at all.
Systems Analyst job is an important part of any company to analyze the business needs, customer needs, user needs etc and translate them into creating a system, software product or a service that customers use. I consider that as the nucleus. You would need to partner closely with business teams on one hand and developers and testers on the other hand, read and research about the specific industry and business segment. You will learn a lot and you will have variety of information to play with.
Wish the very best for your future career, whatever it may be.