I recently came across this word, which Erin McKean (one of the OED editors) defines in "More Weird and Wonderful Words" as: "something the presence of which cannot be verified, usually a disembodied being, because it has no physical effects." But, then I become confused. McKean says it is possibly associated with dragon. I couldn't find anything about that on Google or in the other two dictionaries that cite it (wwftd or Forthrights Phrontistery).

I don't know much about dragons, but why would "drogulus" be associated with them?

This is why. From the OED2:

drogulus (__________).
[Coined _on the spur of the moment' by A. J. Ayer perh. by subconscious association with dragon + L. -ulus as in dracunculus.]
An entity whose presence is unverifiable, because it has no physical effects. Also transf.
1957 A. J. Ayer in Edwards & Pap Mod. Introd. Philos. 608 Suppose I say _There's a __drogulus'' over there,' and you say _What?' and I say _Drogulus,' and you say _What's a drogulus?' Well I say _I can't describe what a drogulus is, because it's not the sort of thing you can see or touch, it has no physical effects of any kind, but it's a disembodied being.'
1959 L. S. Penrose in New Biol. XXVIII. 98, I had difficulty in finding a suitable name for the activated complexes produced in these experiments. On showing one of them to Professor A. J. Ayer, I inquired whether it perhaps might be a _drogulus'._ He replied that it was undoubtedly a _drogulus'."

Oh, thanks, Bear! In other words, there really is no connection.