Ps4 – Getting DLCs from US for Destiny which was bought in Canada

No, the code is bound to your European account and will not work on any other account on your console.

I tried it with a friend's account, who has no code and he logged in on my PS4. It didn't work. Both where European accounts.

Short answer:
Yes, you can.

Longer answer:
From my personal experience. I have two accounts on PS4 - US with PS Plus and European without PS Plus. I bought the game digitally on US account almost on launch and played ever since on EU account (for historical reasons, most of my trophies are there).

You will be able to play normally, but you will miss out on profile-specific exlusive items. For example, before The Dark Below everyone with pre-order got exclusive Sparrow. To use pre-order items like that you'll need to play on account that bougth the game.