Do all root canal treated teeth eventually go black?

I fell and damaged my front teeth last month. After two weeks I had root canals on all four front teeth. I’m now waiting for my permenant all porcelain crowns to be made. I’ve asked my dentist whether I will get a grey line around the crowns and he says no but from reading online I am concerned the teeth that have had root canal will go black underneath and cause a grey line at the gums. I’m hoping because the root canals were done quite soon after this may have stopped them from discolouring as much?