Will Microsoft SQL Server efficiently handle a non-persisted computed column?

I'm having a hard time phrasing this question in such a way that doesn't turn up results for persisted, indexed computed columns.

My question is, if I have a table such as:

CREATE TABLE Customers (
    ID int,
    Name nvarchar(50),
    Balance money,
    HasB开发者_开发技巧alance AS CONVERT(bit, CASE WHEN Balance > 0 THEN 1 ELSE 0 END)
)

Assuming that there's an index on Balance, would the SQL query processor efficiently process a query such as:

SELECT ID, Name, Balance
FROM Customers
WHERE HasBalance = 1

Will it essentially "inline" the computed column expression as if I had specified the case directly in the query?

What about if the computed column's expression were in a non-schemabound user-defined function?

EDIT

My example wasn't great since, as noted, the HasBalance column would not have a very good distribution of data. But ignoring for a moment the efficiency of the index itself, will the query processor basically treat the above query as shown below when selecting an index and choosing an execution plan?

SELECT ID, Name, Balance
FROM Customers
WHERE Balance > 0

It depends on the distribution of the data, right now you only have 2 possible values 1 and 0....so unless you have 99% of the data being one value your selectivity will be very poor, then it has to scan the whole index to find all the positive or negative values

Edit.....Here is what happens, you get a table scan

CREATE TABLE Customers (
    ID int,
    Name nvarchar(50),
    Balance money,
    HasBalance AS CONVERT(bit, CASE WHEN Balance > 0 THEN 1 ELSE 0 END)
)


insert Customers values(1,'d',100)
insert Customers values(2,'d',-2)
insert Customers values(3,'d',-4)
insert Customers values(4,'d',3)
insert Customers values(5,'d',5)

create index ix_test on Customers(Balance)


SELECT ID, Name, Balance
FROM Customers
WHERE HasBalance = 0

set showplan_text on

|--Table Scan(OBJECT:([master].[dbo].[Customers]), WHERE:(CONVERT(bit,CASE WHEN [master].[dbo].[Customers].[Balance]>($0.0000) THEN (1) ELSE (0) END,0)=[@1]))

ANd take a look at this

SELECT Balance
FROM Customers
WHERE HasBalance = 0

--Index Scan(OBJECT:([master].[dbo].[Customers].[ix_test]), WHERE:(CONVERT(bit, CASE WHEN [master].[dbo].[Customers].[Balance]>($0.0000) THEN (1) ELSE (0) END,0)=[@1]))

SELECT Balance
FROM Customers
WHERE Balance > 0

|--Index Seek(OBJECT:([master].[dbo].[Customers].[ix_test]), SEEK:([master].[dbo].[Customers].[Balance] > CONVERT_IMPLICIT(money,[@1],0)) ORDERED FORWARD)