Yes, the global population would be at very high risk.
Consequences would include:
- Direct thermal damage
- Direct pressure damage
- Direct fallout damage
- Indirect damage when countries stop working (lack of infrastructure/eneregy/clean water, collapse of civil society)
- Indirect radiation damage
- Indirect damage through nuclear winter, global cooling, ozone depletion, etc.
- Indirect damage through an extended, 10+ years long famine
Good reference for the above breakdown is The Cold and the Dark: The World After Nuclear War, Sagan, Carl et al., Sidgwick & Jackson, 1985 which in turn is based on Sagan's peer-reviewed article Nuclear Winter: Global Consequences of Multple Nuclear Explosions.
If you look at articles referencing the above, you will find dozens of peer reviewed studies on the subject. They all agree on how deadly this threat is.
The Doomsday clock tracks how close humanity is to self-destruction. Nuclear warfare is the number one threat for our species.
For example, a good, well referenced article on the subject is the following, from Physics today: Environmental consequences of nuclear war, Owen B. Toon, Alan Robock, and Richard P. Turco, Physics Today December 2008, page 37-42
A regional war involving 100 Hiroshima-sized weapons would pose a worldwide threat due to ozone destruction and climate change. A superpower confrontation with a few thousand weapons would be catastrophic
For any nuclear conflict, nuclear winter would seriously affect noncombatant countries. In a hypothetical SORT war, for example, we estimate that most of the world’s population, including that of the Southern Hemisphere, would be threatened by the indirect effects on global climate. Even a regional war between India and Pakistan, for instance, has the potential to dramatically damage Europe, the US, and other regions through global ozone loss and climate change.