As a fairly new museum employee, I guess my experience corroborates your
guess, Deb.  I started off with an internship at the Smithsonian's
National Museum of American History while still an undergrad in history,
about 6 years ago.  Upon earning my BA, I entered a museum studies
program and got an entry-level job doing research for a new museum.
Thanks to having that job, I got a related job as a curatorial assistant
for the firm that was designing the museum.  After a brief stint in
membership at another museum, I returned to the original museum,
participated in the construction and installation, and now have gotten a
promotion to assistant curator.

In other words, I pretty much settled on a museum job from the first,
and have so far been lucky enough to land jobs I like.  I do give a lot
of credit to the Smithsonian internship as a door-opener.