Oh no, to the fact that the eos team doesnt make any real working product i dont believe that it will "kill" ethereum. Of course, ether has some problems with scalability, but it also has the great team which can solve all problems and makes ether the number 1 in crypto space 
I think it all depends on how fast the Ethereum team can solve their current issues whether they can become and stay #1 platform voor dAps. They will not be able to fix it within 2 months, so based on that I would bet on EOS as they will go live around the 1st of June.