Yes. For example, one such filled in grid is:

I've thrown the power of a brute-force sudoku solver at this problem. (Solving puzzles with a program feels a bit like cheating, but since this question is about puzzle createion, I have no qualms.)

The first step was to write a solver that creates all miracle sudokus for an initially blank grid. I didn't bother about symmetrical solutions, because the condition that no two directly adjacent cells can have adjacent numbers rules out the possibility that you can create n sudokus with a 1 in the first cell and then generate 9! · n variations by shuffling the numbers around. I think it is unlikely that condition 3 will survive such a shuffling.

Anyway, it turns out that there are only 72 possible miracle sudokus. The next step is now to save these sudokus as they are generated. Then try to find pairs by comparing the southwest and northeast regions. Again, I wasn't very subtle about it: I used a nested loop that tries all 72×72 possibilities.

The conditions that concern directly adjacent cells are already taken care of by the respective sub-sudokus. Care must be taken when a diagonal king's move or a knight's move goes from the non-overlapping parts from one sub-sudoku to a non-overlapping part from the other. (If you imagine a Venn diagram of two sets, that's a move that goes from (A − B) to (B − A) or vice versa.)

It turns out that there are again 72 possible double miracle sudokus. (The extra care described above does not seem to have an effect, probably because equal numbers are already arranged in a spaced out N-queens-pattern with (3, 1) distances between them.)

I hope I haven't made any mistakes. I've replaced single numbers and stretches of adjacent numbers with hash marks to check whether the conditions are all met. Seems to look okay, but I've only spot-checked.

Now there's the problem of which numbers to fill in initially ...

P.S.: My program and its output are here if you want to check my solutions for errors. Note that ...

... according to my program, there are only 72 possible double miracle sudokus. So once such a sudoku is published, it might be easy to find the answer by just checking the known numbers against this short list.

I think that's generally a problem with sudokus, which are easy to solve mechanically. Still, many people enjoy solving them by hand.

Yes. For example, one such filled in grid is:

I've thrown the power of a brute-force sudoku solver at this problem. (Solving puzzles with a program feels a bit like cheating, but since this question is about puzzle creation, I have no qualms.)

The first step was to write a solver that creates all miracle sudokus for an initially blank grid. I didn't bother about symmetrical solutions, because the condition that no two directly adjacent cells can have adjacent numbers rules out the possibility that you can create n sudokus with a 1 in the first cell and then generate 9! · n variations by shuffling the numbers around. I think it is unlikely that condition 3 will survive such a shuffling.

Anyway, it turns out that there are only 72 possible miracle sudokus. The next step is now to save these sudokus as they are generated. Then try to find pairs by comparing the southwest and northeast regions. Again, I wasn't very subtle about it: I used a nested loop that tries all 72×72 possibilities.

The conditions that concern directly adjacent cells are already taken care of by the respective sub-sudokus. Care must be taken when a diagonal king's move or a knight's move goes from the non-overlapping parts from one sub-sudoku to a non-overlapping part from the other. (If you imagine a Venn diagram of two sets, that's a move that goes from (A − B) to (B − A) or vice versa.)

It turns out that there are again 72 possible double miracle sudokus. (The extra care described above does not seem to have an effect, probably because equal numbers are already arranged in a spaced out N-queens-pattern with (3, 1) distances between them.)

I hope I haven't made any mistakes. I've replaced single numbers and stretches of adjacent numbers with hash marks to check whether the conditions are all met. Seems to look okay, but I've only spot-checked.

Now there's the problem of which numbers to fill in initially ...

P.S.: My program and its output are here if you want to check my solutions for errors. Note that ...

... according to my program, there are only 72 possible double miracle sudokus. So once such a sudoku is published, it might be easy to find the answer by just checking the known numbers against this short list.

I think that's generally a problem with sudokus, which are easy to solve mechanically. Still, many people enjoy solving them by hand.