Is it possible to use deconstruction as a research method to study an organization? Is there any paper which attempted to use deconstruction in this manner?
I would argue that deconstruction is rather a philosophy or methodology for analysing meaning of words, texts, narratives. In this sense, it is closely connected to language and linguistic studies. So it might be difficult to use it for organisational studies in terms of institutional studies. If you e.g. want to analyse outputs of organisations and their meanings, you might well use some deconstructivist approach. If you are interested in the roots and origins of organisations, you might rather use historical institutionalism, or (post)structuralist approaches analysing power and power relations like the ones building on Foucault and others (governmentality studies).
So, it, as often, depends on the specific research question you want to answer.
There is some short discussion on the topic in the following link:
Article Deconstruction as Method in Political Theory
Bankspeak: The Language of World Bank Reports (Moretti and Pestre, 2015) makes no mention of deconstruction (or Derrida) but it is a fascinating study of the changing relationship between text and meaning in that organization (based on quantitative linguistic analysis).
Reference
Moretti, F. & Pestre, D. (2015). Bankspeak: The language of World Bank reports. New Left Review 92 (2). March–April. Retrieved from https://newleftreview.org/II/92/franco-moretti-dominique-pestre-bankspeak
Part of my PhD research methodology used Derrida's deconstructionism (remember that his overall work represents far more than the popular notion of deconstructionism). His work is not a method. The attached article may assist - but might not.