To be precise, acute radiation poisoning first destroys the immune system (proliferating bone marrow and lymphatic cells), followed by the gastrointestinal lining (allowing gut flora to enter the bloodstream and cause sepsis). Recovery is dependent on the patient's ability, with the aid of blood transfusions and broad-spectrum antibiotics, to fight off the infection. Further radiation exposure destroys the cells of the liver, lungs (Simms), kidneys, and nervous system. Neurological symptoms invariably mean death.
So to get a measure of just how screwed the Indus crew is, going off US military projections, the Indus crew can look forward to several months of hospitalization with a mortality rate of upwards of 50% in the best case scenario.
I'm sure the UEF has made great advances in medicine over the past thousand years, but it still takes time to heal and medicine is in short supply. I'm sure their Magical☆Nagari Girl will get priority, though.