When Tether is shut down some day in the future (it is not even a matter of "if" with centralized altcoins, it is a matter of "when") it will definitely cause a lot of panic in the cryptocurrency market as a whole and will create a lot of panic sells that crashes bitcoin price (and consequently altcoin prices). But in the long run nothing will change about bitcoin since as I said in the beginning bitcoin doesn't care about centralized altcoins and what they do.
I don't buy the too big too fail certainty found almost everywhere when thinking of tether. It's big, yes and it can fail.