Does science really ignore the possibility of God?

There is a criticism sometimes levelled at atheists who point to the lack of evidence for the supernatural and therefore gods that the reason they see no such evidence is that they are not looking for it. The suggestion is that the world view on which atheists tend to rely, science, is intrinsically antithetical to supernatural phenomena and does not take their possible existence into account for explanations of the world.
This view is illustrated by Tim Minchin’s eponymous character from the beat poem Storm (see link on sidebar) where she is made to say

”Science just falls in a hole When it tries to explain the nature of the soul.”[…] “Shakespeare said it first: There are more things in heaven and earth Than exist in your philosophy… Science is just how we're trained to look at reality, It can't explain love or spirituality. How does science explain psychics? Auras; the afterlife; the power of prayer?”

Theists in general will tell you that the handiwork of God is all around for everyone to see should we deign to take off our reductionist blinkers and appreciate the awesome wonder of their god’s creation. If only we would look at the world in the ‘right’ way, opening our minds and hearts to the obvious God would be self-evident. However I am going to make an argument that possibly even a philosopher of science would find contentious (at least I’ve never heard it put quite this way) that the scientific method far from ignoring the possibility of supernatural intervention is in fact constantly testing for it.
Science, it is true, presupposes methodological naturalism

Methodological naturalism is concerned not with claims about what exists but with methods of learning what nature is. It is strictly the idea that all scientific endeavors—all hypotheses and events—are to be explained and tested by reference to natural causes and events. The genesis of nature, e.g., by an act of God, is not addressed

which at first sight appear to vindicate the theist’s view that science is ruling anything supernatural out a priori but this ignores the other cornerstones of the scientific method namely falsifiability and the null-hypothesis.
In science a hypothesis is considered to be falsifiable if in principle it can be proved to be incorrect by observation or experiment. For example when J.B.S Haldane was asked what could falsify the theory of evolution he replied ”Rabbits in the Precambrian” by which he meant if a fossil rabbit was found in a geological era prior to the evolution of mammals it would upset the theory.
In practice every experiment conducted or observation made with scientific intent is an attempt to falsify a particular hypothesis but beyond that I would argue they are also, albeit unconsciously, testing methodological naturalism itself because the underlying hypothesis is one of natural cause and effect. A result found or observation made that could not be explained by natural phenomena would falsify methodological naturalism and imply that supernatural events could influence the data.
A null-hypothesis is a statistical concept that states there will be no difference between two sets of observations. For example in a drug trial with a placebo control the null-hypothesis would be that the clinical outcomes will be identical for both groups of patients. An observed statistical deviation between the groups would then tell you something about the effectiveness of the drug in question. For the purposes of this argument I would suggest the null hypothesis that scientific experiments and observations will yield the same results regardless of supernatural or purely natural influences. Over centuries of scientific observations, more than enough to be statistically significant, we have never seen a deviation in an expected outcome due to supernatural activity (Note: I am saying that this null-hypothesis is implicit in the scientific method even if it is not explicit in a particular experiment such as, for example, testing the efficacy of prayer on the mortality rates of cancer patients). This suggests one of two things, either the null-hypothesis is correct and that regardless of supernatural forces the results are identical to those expected from naturalism or, conceivably, there are no supernatural forces. To quote again from Tim Minchin’s Storm

”Throughout history Every mystery Ever solved has turned out to be Not Magic.”

This is not to argue that science has disproved gods or the supernatural but merely to point out that the scientific method is obliquely but consistently testing the hypothesis that is methodological naturalism and as a consequence only ignores the supernatural insofar as, to date, it has either not significantly impacted on observations or shown itself to exist. It is consistent with the rational atheist position that where we do contemplate possible gods they are of the ignorable, non-interventionist, deistic variety rather than the prayer answering, miracle working, null-hypothesis falsifying species beloved of the major religions.