Does WITH SCHEMABINDING on a multi-statement TVF improve cardinality estimates?
In my tests, no, adding WITH SCHEMABINDING does not improve cardinality estimates. I created a simple table:

CREATE TABLE dbo.myobjects(id INT PRIMARY KEY);

INSERT dbo.myobjects SELECT [object_id] FROM sys.all_objects;


Then two functions:

CREATE FUNCTION dbo.noschemabinding(@UserID INT)
RETURNS @x TABLE (id INT)
AS
BEGIN
  INSERT @x SELECT id FROM dbo.myobjects;

  RETURN;
END
GO

CREATE FUNCTION dbo.withschemabinding(@UserID INT)
RETURNS @x TABLE (id INT)
WITH SCHEMABINDING
AS
BEGIN
  INSERT @x SELECT id FROM dbo.myobjects;

  RETURN;
END
GO


Comparing the actual plans, both show estimated rows = 1, actual rows = 2112 (this latter number may differ on your system depending on version/SP etc).

Comparing the speed:

SET NOCOUNT ON;
GO
SELECT SYSDATETIME();
GO
SELECT id INTO #x FROM dbo.noschemabinding(1);
DROP TABLE #x;
GO 1000
GO
SELECT SYSDATETIME();
GO
SELECT id INTO #x FROM dbo.withschemabinding(1);
DROP TABLE #x;
GO 1000
SELECT SYSDATETIME();


Results:

                    run 1               run 2
----------------    ------------------  ------------------
No schemabinding    14632 milliseconds  14079 milliseconds
Schemabinding       14251 milliseconds  13979 milliseconds


So, does it matter much? Nope.

SCHEMABINDING in this case is used for a more important goal: underlying schema stability. You will probably have much better optimization opportunities if you pursue converting your function to an inline TVF than to chase down obscure plan-affecting differences in a multi-statement TVF.