Yes for the rownumber generator, No for the random number generator.

If you want unique but randomly sorted numbers, it will involve a sort (which will be time consuming for as many rows as you've identified) using NEWID() to sort on.

WITH

cteRowNumberGenerator AS

(--==== Prevents sorting all the rows of the cross join.

SELECT TOP (1000) --Put your desired number here

UniqueNumber = ROW_NUMBER() OVER (ORDER BY (SELECT NULL))

FROM sys.all_columns ac1

CROSS JOIN sys.all_columns ac2

)--==== Randomly sorts just the numbers generated from above.

SELECT UniqueNumber

FROM cteRowNumberGenerator

ORDER BY NEWID()

;