Not quickly, the atmosphere itself would actually protect us for a while (I had to look into this to explain to my conspiracy-oriented parents that a pole reversal would not kill everyone). But if the magnetosphere was gone for good, solar wind would strip the atmosphere from the planet over time, as happened to Mars. We would probably all have to retreat to underground caves and domed cities sealed to keep the pressure high enough to live.
We very quickly die from intense solar radiation
Not quickly, the atmosphere itself would actually protect us for a while (I had to look into this to explain to my conspiracy-oriented parents that a pole reversal would not kill everyone). But if the magnetosphere was gone for good, solar wind would strip the atmosphere from the planet over time, as happened to Mars. We would probably all have to retreat to underground caves and domed cities sealed to keep the pressure high enough to live.