As literally stated, no this could not have been the case.
Let's take the Wikipedia list of wars by death toll, and take the maximum estimate of each (almost certainly too high) in the 20th Century. Let's consider only wars with over a million deaths.
- Second World War: 85 million
- Second Sino-Japanese war (almost certainly some overlap with WWII) 27 million
- World War 1 30 million
- Chinese Civil War (probable overlap with Sino-Japanese) 7.5 million
- Russian Civil War 9 million
- Second Congo war 5 million
- Algerian War of independence 2 million
- Korean War 1 million
- Vietnam War 4 million
- Nigerian Civil War 3 million
- Mexican Revolution 2 million
- Sino-Tibetan War 1 million
- First Indochina War 1 million
- Iran-Iraq War 1 million
- Second Sudan Civil War 1 million
- Soviet Afghanistan War 1 million
- Mozambican Civil War 1 million
- Rwandan Civil War 1 million
- First Congo Civil war 1 million
- Spanish Civil War 1 million
- Mozambican Civil war 1 million
Horrific as these figures are, they come to less than 200 million deaths. The world population grew to 1 billion around 1830, which makes it more than certain that there were many more than a billion deaths before 1900.
It is of course possible that they author meant to say "more people died in wars in the 20th Century than in all previous wars". That's going to be much harder to calculate, because of some very vague statistics of deaths in ancient wars, but also a vague definition of 'what is a war'. If one village rides out to kill the people in another village and steal their cows, that doesn't count as a war in twentieth century reckoning, but it may have happened millions of times in the ancient world and the casualties add up.