No. It's, "here, this medication can protect you from radiation for x-hours. After that there's nothing that can be done and you'll begin absorbing the radiation and feeling the effects of it, after which you'll be dead within a day."
It wasn't a countdown to death it was a countdown to the time when there's nothing that can be done medically to protect you from the radiation exposure.
Doctors in hospitals wear a little pin called a dosimeter. It's basically a piece of film that changes color depending on how much radiation exposure it (and thus the wearer) has while wearing it. So a doctor accidentally walks into a room while an X-Ray is on and the thing changes color a little bit, telling the doctor he's been exposed to radiation so he knows to either get treatment or be careful as his body recovers from the exposure.
But say he walks in on, I dunno, the room where the CAT machine is and explodes or something. The dosimeter goes, "Holy FUCK!" and shows whatever represents lethal exposure. This tells the doctor he got a heavy dose of radiation and that he's fucked. He doesn't die right away, he just knows that his death is imminent from the lethal exposure. The dosimeter being more vulnerable and quicker to reveal the exposure than the cells in his body are to start failing and cause sickness.
That's what the "countdown" is. It's the Enterprise's dosimeter. It's not counting down to death it's counting down to "point where there's nothing we can do." Hell, I don't think there's ANY level of radiation exposure that causes instant death, maybe at most it'd be in the terms of hours. But not instant.
During the episode Crusher was doing what she could do to stay off the radiation effects. (Whatever drugs/methods that may be.) Afterwards there may be things she can do to reverse the damage. The computer was counting down to the point where medical science simply couldn't do anything for you, you've been exposed to too much, get your affairs in order.