Your thinking is correct. Take the below example on a non-indexed view:
To create the test view:
use AdventureWorks2012;
go
create view dbo.DepartmentView
as
select
Name,
GroupName
from HumanResources.Department;
go
Now if you were to look at the execution plan of a SELECT on the view:
select *
from dbo.DepartmentView;
You can see below that the index of the underlying table is referenced (HumanResources.Department):

Likewise, when you update the view, you will see similar behavior:
update dbo.DepartmentView
set GroupName = 'QA'
where GroupName = 'Quality Assurance';

You can also write a few queries against the system catalog views to show that the only thing that is persisted is the definition of the view:
-- see the object in sys.objects
select *
from sys.objects
where object_id = object_id('dbo.DepartmentView');
-- ensure there are no indexes related to this view object
select *
from sys.indexes
where object_id = object_id('dbo.DepartmentView');
-- the definition is persisted
select
object_name(object_id) as object_name,
definition
from sys.sql_modules
where object_id = object_id('dbo.DepartmentView');