As it turns out, no, it does not. And this surprised me. The Oxford English Dictionary does not actually supply a definition for the word "everything," just discussion of its operation as a word:
A combination of
every adj. and pron. 1 and
thing n.1 As in
anything,
something,
nothing,
the subst. element has usually no definable meaning, the compound being equivalent to a neuter absol. use of the adj. The distributive sense etymologically belonging to the word is often absent, its force being merely collective; hence it is the current substitute for
all (absol.),
all things, which in most contexts are now somewhat formal.
Note the section I've bolded. At the very least the
thing part of the word is explicitly said to have no meaning.
But note also that no definition is given and that the best the dictionary does is give a phrase for which it can serve as a substitute.
Everything, it turns out, doesn't mean anything.
Hope that clears everything up.
.