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Depend what kind of radar system they have.

As for the consequence of a nuclear attack, here is a gist of what will happen:

Short Term

Median Lethal Dose (LD50): When comparing the effects of various types or circumstances, that dose which is lethal to 50% of a given population is a very useful parameter. The term is usually defined for a specific time, being limited, generally, to studies of acute lethality. The common time periods used are 30 days or less for most small laboratory animals and to 60 days for large animals and humans. It should be understood that the LD50 assumes that the individuals did not receive other injuries or medical treatment.

Initial radiation from fallout can exceed 300 gray per hour (Gy/h) immediately downwind of a ground burst. A cumulative dose of 4.5 Gy is fatal to half of a population of humans. There have been no documented cases of survival beyond 6 Gy. Most people become ill after an exposure to 1 Gy or more. The fetuses of pregnant women are vulnerable and may miscarry, especially in the first trimester. Human biology resists mutation from large radiation exposure: grossly mutated fetuses usually miscarry. Civilian dose rates in peace-time range from 30 to 100 µGy/y.

Fallout radiation falls off ('decays') exponentially (quickly) with time. Most areas become safe for travel and decontamination after three to five weeks.

The most dangerous emissions from fallout are gamma rays, which travel in straight lines, like ordinary light. The fallout particles emit the invisible, deadly gamma rays in the same way that a light bulb emits light. Gamma rays are invisible, and cannot be seen, smelt, or felt. Special equipment is required to detect and measure gamma rays.

For yields of up to 10 kt, initial nuclear radiation is the dominant casualty producer on the battlefield. Humans receiving an acute incapacitation dose (30 Gy) will become performance degraded almost immediately and ineffective within several hours. However, they will not die until 5 to 6 days after exposure assuming they do not receive any other injuries which make them more susceptible to the radiation dose. Individuals receiving less than a total of 1.5 Gy will remain effective. Between those two extremes, people receiving doses greater than 1.5 Gy will become degraded; some will eventually die.

A dose of 5.3 Gy to 8.3 Gy is considered lethal but not immediately incapacitating. Personnel exposed to this amount of radiation will become performance degraded within 2 to 3 hours, depending on how physically demanding the tasks they must perform are, and will remain in this degraded state at least 2 days. However, at that point they will experience a recovery period and be effective at performing non-demanding tasks for about 6 days, after which they will relapse into a degraded state of performance and remain so for about 4 weeks. At this time they will begin exhibiting radiation symptoms of sufficient severity to render them totally ineffective. Death follows at approximately 6 weeks after exposure.
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Long Term

Late or delayed effects of radiation occur following a wide range of doses and dose rates. Delayed effects may appear months to years after irradiation and include a wide variety of effects involving almost all tissues or organs. Some of the possible delayed consequences of radiation injury are life shortening, carcinogenesis, cataract formation, chronic radiodermatitis, decreased fertility, and genetic mutations.

Link to the rest of Nuclear Fallout