Tether is Tether. Bitcoin is Bitcoin. The fact that exchanges exist which allow you to trade one for the other does not make them the same kind of thing.
Tether printing is a convenient way to inflate the exchange rate. Remove Tether printing and the exchange rate falls.
As long as people talk about Bitcoin in terms of the exchange rate, Tether and Bitcoin are deeply connected.
So, no, it would still tank the price, because the price is quite likely inflated through fraud.