CASE statement and SARGability - specific use case
From experience I would expect the index not to be used in the query against the view. However, to determine if something is SARGable you just need an example query against a data set for which the index is beneficial. So, best to test it.

First I'll create some test data:

CREATE TABLE dbo.tblStates (
StateAbbreviation VARCHAR(2) NOT NULL,
FLUFF VARCHAR(10) NOT NULL
);

-- insert all possible abbreviations to future-proof table
INSERT INTO dbo.tblStates WITH (TABLOCK)
SELECT CHAR(t1.number) + CHAR(t2.number), REPLICATE('Z', 10)
FROM
(
    SELECT number
    from master..spt_values
    WHERE number BETWEEN 65 and 90
) t1
CROSS JOIN 
(
    SELECT number
    from master..spt_values
    WHERE number BETWEEN 65 and 90
) t2;

CREATE INDEX IX_TBL_STATES ON dbo.tblStates (StateAbbreviation);


When running this query we can see that the index is used to do a seek:

SELECT StateAbbreviation
FROM dbo.tblStates
where
StateAbbreviation in ('AK', 'TX');




However, if we create a view:

CREATE VIEW STATE_VIEW
AS
select 
  StateAbbreviation
  , IsBig = case when StateAbbreviation in ('AK' , 'TX') then 1 else 0 end
from tblStates;


The equivalent query no longer uses the index to seek:

SELECT StateAbbreviation
FROM STATE_VIEW
where IsBig = 1;




db fiddle link is here.