I'd say no. However, if that rumored Captain Pike show ever comes into being, I do think there's the potential of hurting DIS tremendously. I say this because the two shows would take place in the same time period in roughly the same sector of space (unless DIS skips off due to a spore drive malfunction somewhere else). Also, DIS slowly moved away from the "lower decks" format over the season, and seems like it's going to settle into the Trek norm of bridge crew as main cast. While they still could have the shows differ a bit in tone and structure (e.g., Pike Trek as more of an ensemble, a bit more semi-episodic, etc) there would be precious little to distinguish the two, making it easy for CBS to shitcan whichever show wasn't working (and find some way to transfer over the more popular characters to recurring - or even starring - roles on the other).