I just made an account here to answer that question.

If you load a save file from someone with the DLC, without having the DLC yourself, the stuff that you get from the DLC will just disappear.
Example: If you load a save that was made with a DLC to have all 4 cooking pots, and the 200 coin/day setup.
Onto a fresh install of pokemon quest on a new user: You get all the pokemon that the save has, but the cooking pots and the coin bonus will not be there.
How do i test this myself without homebrew?
Easy: Sign out your nintendo user that has the DLC's Log into a new account. "Download" the game from eshop (free) on the new account. Start the game.
You will notice that it uses the save from your other account, but the DLC stuff will be gone.
Conclusion: If you load a save from someone else using a DLC, unless you have the DLC yourselves. You will get everything besides the DLC content.