It may be feesable if the arduino can keep up. Make sure your level shifter can handle the speeds you are trying to use, and a lot of level shifters are either open drain, or do not have enough current for anything. If yours is open drain there needs to be pull ups and if there isn't enough current then you just can't talk.
I do not know enough about DMX to give you a solid answer but those are some things to look at.