Okay according to ye-olde Memory Alpha: http://en.memory-alpha.org/wiki/Elizabeth_Cutler
Yes, it was a situation comparable to when the Voyager Doctor trained-up Paris as an interim medic.
There are episodes when Phlox and others state in dialogue that she's functioning as a "medic" (even though her actual job is in entomology, but hey, she's in the biology division blue-shirts so that's better than training up a security guard). And in "Two Days and Two Nights", she's officially being the acting-Doctor for the skeleton crew while Phlox is hibernating (though they point out she isn't that great at it and needs to wake up Phlox).
So my functional guess is that she was indeed intended to be the "nurse" character, they talk about her in interviews as his nurse, but when the actress died, out of respect they didn't want to kill off the character as well -- thus the explicit mention precisely once in early season 3 that Cutler is still alive. So I guess because the actress died she's just "in the other room".
Still, you'd think they'd have some extras helping Phlox in seasons 3 and 4.