Do temporal tables log changes when there are none?
Converting my comment to answer .. 

If the value is actually updated, then it will log changes. If you update the same value, new versions for every row will be recorded, but the column values will remain the same.

Below is the working example :

CREATE TABLE dbo.blah1
    -- PK is a requirement !!
    (
    foo INT identity(1, 1) PRIMARY KEY
    ,baa INT
    ,SysStartTime DATETIME2 GENERATED ALWAYS AS ROW START NOT NULL
    ,SysEndTime DATETIME2 GENERATED ALWAYS AS ROW END NOT NULL
    ,PERIOD FOR SYSTEM_TIME(SysStartTime, SysEndTime)
    )
    WITH (SYSTEM_VERSIONING = ON);

-- insert data
insert into dbo.blah (baa)
values (1)


Now check for the data

-- check data
    SELECT * FROM  dbo.blah;
    select * from [dbo].[MSSQL_TemporalHistoryFor_629577281]




perform dummy update

update blah 
set baa = baa




Perform onemore dummy update .. there will be rows with same values but different systime - start and end.



You have to have a proper mechanism to clean up history table as that can grow significantly larger if you forget to trim it.