Should we consider aliens as a scientific explanation for unexplained phenomena? Or is it outside the scope of what should be termed a scientific explanation?
Solely collecting information and theorizing is not exactly science. Science encapsulates both the organization of knowledge and a positive method to collect and interpret information.
That is, unless you perform any statistically solid experimentation, you are not doing science. The process through which you come up with a logical explanation based on some evidence is termed a "hypothesis", which can be scientific or non-scientific. If you perform controlled experiments and test that hypothesis, you are making it a valid scientific process. Simply, if it is not testable, it is not science. This also is one of the reasons why science is our most reliable way of gathering information. If you don't believe me when I say "when you drop a ball it falls", you can test it and see for yourself. This testable property of science is also why it is so closely tied to statistics, as uncertainty is an inherent property of many real-world questions.
Aliens as an explanation to unexplained phenomena is outside the scope of science mostly because of this reason. You can propose it as an explanation, i.e. form an hypothesis, but it will not be scientific because you cannot test it by performing experimentation. Science also disregards any anecdotal evidence because of this reason as well. For example, Freud got a lot of criticism because of that, in spite of the fact that his explanations are absolutely practical. However, aliens as an explanation to unexplained phenomena is not completely illogical. It is so, as long as what you propose is not in conflict with basic physical laws.
Other topics which are outside the scope of science are so because they are not testable, for example: The existence of a God, the nature of qualia, simulation theory (which in my opinion is not dissimilar to the first one), problem of other minds, so on and so forth, in addition to aliens.
Any parsimonious explanation that agrees with observation may be scientific. It depends on how much evidence you have. It's silly and unscientific to say, "Gosh, the Pyramids would have been really hard to build... can't see how the Egyptians managed it. Must have been aliens."
However, if aliens land in Times Square and pass out ray guns, it would be unscientific to deny them. Or more likely, if we find a signal from outer space that can be decoded as language, then it's scientific to suppose aliens produced it.
As yet, there's not much actual evidence of aliens, and proposed theories about them are speculative.
The only scientific discipline where aliens are even remotely considered is astronomy, when some new phenomenon is observed, displaying a novel and unexpectedly complex or patterned signature, and for which no known natural phenomenon offers a tenable explanation.
For example the first pulsar to be discovered was thought to be possibly of alien origin, until the phenomenon became better understood.
At the other end of the scale, at one time the presence of organic molecules in meteorites and other objects in the solar system was conjectured to suggest that the Earth was seeded with life from space, but this theory has since been discredited.
But as for unexplained terrestrial phenomena, no, aliens are as unacceptable to science as phlogiston or N-rays.