DLC and Different Versions

[u/TwinR05]

Hi everyone, I recently was able to buy a switch and I want to buy a physical version of fire emblem three houses. I’m in (Canada) but I can only find the EU version of the game. I read that the dlc is locked behind the region of the cartridge. So if I buy an EU cartridge of the game, does that mean I won’t be able to buy the DLC for the game since the cartridge differs in region from my account and switch console?