It’s an interesting question. I think that the answer is probably no.
Underneath the Earth’s crust (the first layer) there is a liquid layer called the mantle. Because it’s liquid, the hole will seal up again.
At the moment, the deepest hole we’ve ever drilled is the Kola Superdeep Borehole in Russia and is 12262 m deep. To get to the center of the earth, we would have to drill 6400000 m deep!
Here’s an awesome video that shows you some of the world’s deepest holes: https://www.youtube.com/watch?v=fiW4gnaqCv4
In the future I think maybe, but in our lifetime probably not! It’s 2000 miles to get to the core! The furthest we’ve gone is 12km. Also we’d have problems when we get there as it’s around 11,000 degrees fahrenheit (the same as the surface of the sun) and the pressure at the core is the same as 48,000 elephants sitting on you!