No, space exploration does not disprove evolution. Indeed, my first reaction on seeing this title was complete bafflement. Evolution holds that the characteristics of animals have come about through there being advantages to those characteristics. If a long beak provides an advantage in extracting nectar from a plant, then individuals with a long beak will be more likely to thrive and attract a mate, and thereby pass on the genes for a long beak.
Humans, on the face of it, don't look like a likely candidate to be the world's dominant species. After all, we are not that strong and can't run that fast. However, we were able to use our big agile minds to our advantage and big agile brains have therefore become a feature of our species as we've progressed from homo erectus through to homo sapiens cavemen and through to modern day humans. It is precisely this evolution that has made us capable of engaging in space exploration.
I guess though that the creator of this title was hinting that a failure to discover other life-forms beyond our home planet might signal the deathnell of evolution? The insinuation would be that there is something special about Earth, indicating that its life-forms (and particularly humans) were created by the intelligent design of a supernatural god.
The likelihood, however, is that space exploration will bring confirmation that there is life (and once was life) on other planets and moons in our universe. For example, the presence of water is often considered to be one of the perquisites of finding extraterrestrial life and Jupiter's sixth moon, Europa, is believed to have a water ocean beneath its icy smooth surface. That's at least one candidate within our own solar system but as the search for extraterrestrial life expands beyond our very small corner of the universe the number of candidate planets expands exponentially.
Research by the UK's Open University identified that out of 100 studied stars with planets circling them, "there are perhaps 50 or so of these small, rocky bodies on which there is liquid water and possibly life." The scientists talk about planets that exist within a so-called Goldilocks zone (i.e. not too hot and not too cold!) and state that they would "certainly expect them to be something like Earth in size and in mass, to have a reasonable atmosphere; they'll have oceans and continents, they'll be potential abodes of life". Gliese 581 d, for example, is a planet that is considered likely to exist within a habitable zone where "liquid water, and therefore, life, could exist". At 20 light years away, however, it may be some time before humankind is capable of properly exploring this interesting habitat! (Note: It is estimated that the Milky Way contains in the region of 100 to 400 billion stars, of which we are only able to observe a fraction.)
The existence of other life-forms will not, however, end the debate on evolution. Religious opponents of the concept of evolution would no doubt simply say that their god also created those other life-forms. What space travel will do, hopefully, is shed further light on the universe that we live in. It may prove that Earth is very unusual with its diversity of life, or it may show that we're just one of many outcrops supporting a rich abundance of life. The battleground for the evolution debate, however, will remain firmly planted on planet Earth, with discussion of the evidence that has been compiled from our home planet.