No. Science can only prove or disprove the existence of physical things – that is, things made of matter that take up space. But angels are not physical beings, like humans; they are pure spirit.
At best, people who refuse to use any method except science to acquire knowledge must remain “agnostic” (or uncertain) about the existence of angels since science is incapable of answering such spiritual questions. In other words, there is an absence of scientific evidence for the existence of angels; but only because science cannot produce evidence for angels since angels are not physical beings.
A skeptic might say “There is absolutely no scientific evidence for angels, therefore angels do not exist.” But this is a poor argument because absence of evidence is not evidence of absence. For example, if I walk through a friend’s home without leaving a trace of evidence behind that I was there, it does not follow that I was never there since I left no evidence of my past presence. It just simply means there is no evidence and whether I was there or not is left undetermined.
Science works to explain things or occurrences in the natural world (like flowers and magnetism), not things or occurrences in the supernatural world (like angels or levitation). The scientific method allows us to make observations and form “educated guesses” about causes and effects involving time, matter, space and energy, like how water evaporates or whether atoms exist.
But as soon as we start to ask questions about non-physical or “spiritual” things, like souls or angels, we must resort to other ways of uncovering evidence, like theology, philosophy and history to find proofs and explanations. This is why priests study philosophy and theology in seminary – because they are in the “business” of spiritual things.