In theory yes, but layouts that require just filling in missing numbers are not puzzles. The layouts with missing numbers become puzzles when some thought must go into entry selection. The question is how many puzzles requiring logical deductions are there for each unique 81*81 grid.
At first approximation, the number of logical deductions just goes up (exponentially?) with the number of missing digits. That's why you see many sudoku books grouping puzzles by "difficulty" by just stating how many digits are given.
Of course humans can make much more interesting puzzles, where you are expected to make a certain string of logical deductions to reach the solution. But simple "machine-made" sudokus seems to sell well enough, so I see no reason to exclude them from the definition.
