not only do i not have formal work experience in public health (or health care in general), i'm also graduating early from undergrad, yet i was accepted into almost all of the programs i applied to. i'm attending unc-chapel hill next year. i think if you can prove yourself and make up for the "lack of experience" elsewhere, you'll be fine. at the same time, i did have a diverse research-track from neuroscience to finance and a public health minor. i think it will ultimately depend on whether or not your background fits into what the program you're applying to requires. you may lack work experience but have other qualities to offer them.
by the way, to add to snoofle's comment. indeed, the average age for the hpm track is quite high, since most students gain work experience before attending. in fact, during an interview, i was told i was almost rejected during the first round of review due to my lack of experience... yet a few weeks after, i learned that i was offered a scholarship.. (??) strange, but anything can happen.
certain programs do REQUIRE that you have work experience, i think a few have been mentioned already. for instance, the mph in health management at johns hopkins canceled my application, because i didn't have any (but they didn't give me back my application fee!! jerks) .. i was given the option to re-do my application for the mhs instead, but i was too lazy and not interested in johns hopkins enough.