My experience is that in JQM 1.0 and 1.0.1 they persist.
In 1.1 and 1.1.1, they don't. Maybe technically, they do, but they go with the transition. That is, say you do a slide transition. In 1.0, the footer stays put, and the rest of the page slides above it. In 1.1, the entire page, including the footer, slides.