I believe her conversation afterwards indicates that it's more like she was possessed and the TARDIS kept her safe, as it was her plan to save The Doctor.
We know that the TARDIS is conscious (6x04 The Doctor's Wife), and Rose also seems to indicate this in her line:
I looked into the TARDIS, and the TARDIS looked into me.
Sure, the Doctor corrects her ("You looked into the time vortex. Rose, no-one's meant to see that."), but it may be that The Doctor simply doesn't realise this yet (As until The Doctor's Wife, it had been established that only later model TARDISes were known to be conscious).
With all this in mind, I think it makes her final conversation with The Doctor more meaningful:
Rose: What happened?
The Doctor: Don't you remember?
Rose: It's like. . .there was this singing.
The Doctor: That's right, I sang a song and the Daleks ran away!
Rose: I was at home... No, I wasn't, I was in the Tardis and there was this light. I can't remember anything else.
There are also similarities between the look of the "essence" that The Doctor removed from Rose and blew back into the TARDIS, and the "essence" of the TARDIS escaping from Idris in The Doctor's Wife:
As to why it still caused The Doctor to die, that may be because Time Lords are already operating on a similar plane of consciousness to the TARDIS, as the Doctor hints at:
Rose: I can see everything. All that is, all that was, all that ever could be.
The Doctor: That's what I see, all the time.
Which would make the effect of having another consciousness inhabit their own even more stressful on their physiology than on a human.