Would this crash the stock market? Probably not.
Would it be the top breaking news? Probably at least for a little while. I think it wouldn't be any more shocking than any of a number of mass attacks on our western society and way of living by terrorists though.
Would it bring into question how we came into contact with the aliens? Yes. If Trump announced we had a secret space program and military personnel already traveling to different star systems with reverse engineered Allen tech, then I could imagine foreign governments asking us to share the discoveries. Our government doesn't like to share. I guess the plan is to keep it all secret and not let the president know but what if too much information already leaked out? Would they try to discredit the info the president had and make him look foolish announcing something with no proof? It could get interesting.
If we had a secret space program and were acquiring alien tech, should it all remain secret? Would Trump or Hillary both spill some beans? It could get interesting.
Lol, Trump's proof probably would be a picture of a Trump building on a planet with two moons or two Suns or something dramatic. Real estate deals in an alien city.