Or phrased differently, are non-symmetrical Sudoku puzzles considered legal?
Any sudoku puzzle with enough numbers filled in that the solution is unique is considered a "valid" or "legal" sudoku. Before some time in 2005, the Toronto Metro newspaper published sudoku puzzles (although not named Sudoku at the time) where exactly four numbers in each row, column, and 3x3 square were filled in, and those were never rotationally symmetrical.
However, the sudokus that newspapers tend to publish usually have some form of symmetry, usually for aesthetic reasons. Usually this symmetry is rotational.
Yes, non-symmetric Sudoku puzzles are valid. For example:
This is a minimal Sudoku puzzle, with exactly 17 clues, and is not symmetric.
Image courtesy of the Wikimedia Commons.