Definitely yes.
I'm the kind of person that believes in pretty much everything, even if I know for a fact (not Fact) that it's not real. When some people say "suspension of disbelief" when talking about fiction, I have nothing to suspend
This is something that used to drive my parents crazy. They said that I live in two worlds at the same time (
two! More like a dozen!), and I really have to stop it. I didn't; I just learned how to hide it.
I know many people who view myths and mythologies as just stories. Fairy tales. I'm also fascinated by all kinds of myth(ologies) from a story point of view, but for me they are also
true. This creates a cotradiction, because myths of different cultures are contradictory, so you could say that I believe in nothing. *shrugs*
So yes, I believe in Tolkien's mythology. I don't try to find it in our world that we call "real", but I know it's there. Probably more so than most other mythologies. At least for me.