Does Animal Crossing know that the system time was changed if I put it back?

All Animal Crossings games check the time difference when the game is loaded up.

When you start the game, it checks the difference between the last time it was started and now and acts upon this difference (like, adding fossiles in the ground, creating a bunch of weed, populating your mailboxes etc.).

That's why, when the first time starting the game each day, the loading time is a bit longer.

Your procedure should be OK as long as AC is not running and nobody starts it while the clock is set back.

It's even something my SO regularly do to "not miss" an AC day (go back in time, play the day you missed then put the clock back on synchronize).