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It's best to take the questions in reverse order: Do [we] include information from corpus research [in our responses to questions]?
Yes. The Grammar Exchange team uses the Longman Grammar of Spoken and Written English by Douglas Biber and four other authors,* which is an excellent source of information from corpus research. The corpus used by the team of authors"”known as the Longman Spoken and Written English Corpus (LSWE)"”consists of more than 40 million words, representing four registers: spoken language, fiction, newspaper language, and academic prose.
In addition to this resource, the Grammar Exchange team often uses a Web search engine to find relative frequencies of words and grammatical constructions on the Internet. Finally, we have at our disposal the COBUILD Concordance Sampler, which returns up to 40 examples of these kinds of items, from corpora of different genres, both spoken and written, and both British English and American English.
The first (but second here) question is: How common are that- noun clauses in subject position in written academic discourse?
The answer is "not common at all."
First, to illustrate noun clauses in subject position, here are two examples from a Google search:
"That nothing has been done is loathsome, and reflects as badly on Congress as a whole as any one member or group of those sharing similar views. ..."
"The importance of this building is that, in comparison to the Ökohaus in Frankfurt, which was fundamentally an experimental scheme, this project is an investors' building with their ensuing stringent financial requirements. That this is so has perhaps weakened the strong, more radical aesthetic as seen in the Frankfurt project."
Biber et al. report that such clauses in subject (or "pre-predicate") position "are rare in all registers. They occur 10-20 times per million words in academic prose and news while they are virtually nonexistent in conversation "(p. 676). The two genres where they occur most are news, especially sports writing, and academic prose, but 10-20 times per million words is not an impressive frequency.
Here is an example of a pre-predicate noun clause from Biber et al.:
"It became surprisingly apparent that all meteorites are of the same age, somewhere in the vicinity of 4.5 billion years old [...] That there are no meteorites of any other age, regardless of when they fell to Earth, suggests strongly that all meteorites originated other bodies of the solar system that formed at the same time that the Earth did (ACAD)" (pp. 677-8)
The principal purpose of these clauses is to introduce factual material that relates closely to the preceding discourse. A much more frequent construction to accomplish this purpose ("500 times per million words in academic prose" (Biber, et al., p. 676) is the similar phrase "The fact that..."as in this example from Biber et al.:
"The fact that 14 of the 29 questions were answered correctly by 30 per cent or more of the lowest band suggess that there is a range of questions within the conceptual grasp of all or practically all the lowest band of attainers (ACAD)" (p. 676)
Douglas Biber, Stig Johansson, Geoffrey Leech, Susan Conrad, and Edward Finnegan. Longman, 1999