Yes, I do believe that Trump can be President regardless of his views on Science. I personally have not heard any statement where Trump stated he did not believe in Science. If that was a true statement he made, I would have to understand more about where he was coming from. Either way to run this country does not involve anything scientific. He would need to use his business smarts and understanding of the laws more than anything.
Yes, Trump can be president even if he doesn't believe in science. There is no requirement anywhere that requires a president to share in any belief other than the US Constitution. However, his lack of belief in science, and more specifically in global warming is a bit of a red flag. It shows that he is not willing to listen to experts and that he is not likely to use common sense and judgement.
Trump's proclamation that he doesn't believe in science demonstrates the strong anti-intellectual streak that his campaign believes is so popular among the public. However, most members of the American public do not believe that someone who is wilfully ignorant should making important decisions relating to the future of the population.
If Congress supported Trump in slashing funds for the EPA or changing the law to remove the agency’s power to regulate, there are predicts that there would be an outcry from overwhelmed governors and reasonable people who care about their families, their children and their life style. Imagine what a future with fewer or less effective vaccines might look like...