The earliest Armageddon games I can find go back to the Women's World Chess Championship 2001, and the FIDE World Championship in 2002, which GM Ruslan Ponomariov won. This is probably a fairly complete list since Armageddon really only lends itself to knock-out tournaments or matches, and the question did ask primarily about GMs and Armageddon. There might be the occasional country championship that goes to tiebreaker, which I did not find, similar to when GM Irina Krush lost to IM Anna Zatonskih in 2008 for the U.S. Women’s Championship in a controversial finish.
So, while these stats may not be 100% complete, they can give a good idea about the overall statistics.
I am amazed by the results of this: Out of the 48 games I found, 24 were 1-0, 15 were 0-1, and 9 were ½-½. If you look at that both the 0-1 and ½-½ count as wins for black, then the result was exactly 24-24. Seemingly quiet a fair tiebreaker system.
Here is the data I used to compile this estimate.
FIDE World Chess Championship 2002
This was the only FIDE World Championship to use Armageddon during the period of when Kasparov broke off with the title until it was unified in 2006. Prior to this, in 1998 and 2000, they continued playing additional blitz games, and in 2005, FIDE reverted to a double-round-robin tournament.
GM Zoltan Gyimesi defeated GM Stuart Conquest 4-3 in round one. Gyimesi had white 1-0.
GM Emil Sutovsky defeated GM Alonso Zapata 4-3 in round one. Sutovsky had white 1-0.
GM Lazaro Bruzon defeated GM Liviu-Dieter Nisipeanu 4-3 in round one. Bruzon had white 1-0.
GM Jaan Ehlvest defeated GM Ilia Smirin 4-3 in round three. Ehlvest had white 1-0.
GM Alexey Shirov defeated GM Veselin Topalov 4-3 in round four. Shirov had black 0-1.
Chess World Cup 2005
GM Yuri Shulman defeated GM Vadim Zvjaginsev 3.5-3.5 in round one. Shulman had black ½-½.
GM Predrag Nikolić defeated GM David Navara 3.5-3.5 in round one. Nikolić had black ½-½.
GM Sergey Erenburg defeated GM Zviad Izoria 4-3 in round one. Erenburg had black 0-1.
GM Evgeniy Najer defeated GM Shakhriyar Mamedyarov 4-3 in round two. Najer had white 1-0.
GM Yuri Shulman defeated GM Vadim Zvjaginsev 3.5-3.5 in round two. Shulman had black ½-½.
GM Sergei Tiviakov defeated GM Oleg Korneev 4-3 in round two. Tiviakov had white 1-0.
GM Loek van Wely defeated GM Alexander Moiseenko 4-3 in round two. van Wely had white 1-0.
Chess World Cup 2007
GM Michael Roiz defeated GM Varuzhan Akobian 4-3 in round one. Roiz had white 1-0.
GM Konstantin Sakaev defeated GM Nikita Vitiugov 4-3 in round one. Sakaev had black 0-1.
GM Zhou Jianchao defeated GM Andrei Volokitin 4-3 in round two. Zhou had white 1-0.
GM Kiril Georgiev defeated GM Rustam Kasimdzhanov 4-3 in round two. Georgiev had white 1-0.
Chess World Cup 2009
This year, by some accounts a mistake, the tiebreaker was changed to four rapid games, then up to five pairs of blitz games, and only then, Armageddon. Not surprising, but there were no Armageddon games, however, GM Varuzhan Akobian did defeat GM Pavel Tregubov 9-7, just one game short of Armageddon.
Chess World Cup 2011
Starting this year, they went back to the previous tiebreak format, but with two shorter 10+10 rapid games added after the 25+10 rapids.
GM Yuri Drozdovskij defeated GM Alexander Motylev 5-4 in round one. Drozdovskij had white 1-0.
GM Leinier Domínguez Perez defeated GM Igor Lysyj 5-4 in round three. Domínguez Perez had white 1-0.
Chess World Cup 2013
GM Evgeny Tomashevsky defeated GM Alejandro Ramírez 5-4 in round one. Tomashevsky had white 1-0.
GM Julio Granda defeated GM Hrant Melkumyan 5-4 in round one. Granda had black 0-1.
GM Daniil Dubov defeated GM Ruslan Ponomariov 5-4 in round two. Dubov had white 1-0.
Chess World Cup 2015
GM Gabriel Sargissian defeated GM Mateusz Bartel 4.5-4.5 in round one. Sargissian had black ½-½.
GM Michael Adams defeated GM Viktor Láznička 5-4 in round two. Adams had white 1-0.
GM Hikaru Nakamura defeated GM Ian Nepomniachtchi 5-4 in round three. Nakamura had black 0-1.
Chess World Cup 2017
GM Levon Aronian defeated GM Maxime Vachier-Lagrave 5-4 in the semi-finals. Aronian had white 1-0.
Chess World Cup 2019
GM Anish Giri defeated GM Evgeniy Najer 5-4 in round two. Giri had black 0-1.
GM Yu Yangyi defeated GM Nikita Vitiugov 5-4 in the quarter-finals. Yu had white 1-0.
Women's World Chess Championship 2001
Note: I could not confirm the format with 100% accuracy. I am reasonably guessing that this used the same format as the men, and the women in 2008, which I could confirm. In addition, the brackets had the 4-3 results as in the men’s tournaments.
GM Zhu Chen defeated GM Maia Chiburdanidze 4-3 in the semi-finals. (no data)
Women's World Chess Championship 2004
GM Peng Zhaoqin defeated IM Joanna Dworakowska 4-3 in round one. Pend had black 0-1.
WGM Ketino Kachiani defeated WGM Nguyễn Thị Thanh An 3.5-3.5 in round one, Ketino Kachiani had black ½-½.
IM Tatjana Vasilevich defeated WGM Xu Yuanyuan 4-3 in round one. Vasilevich had black 0-1.
IM Lilit Mkrtchian defeated then WGM Monika Soćko 4-3 in round one. Mkrtchian had white 1-0.
Then WGM Kateryna Lagno defeated then untitled Ekaterina Atalik 4-3 in round two. Lagno had black 0-1.
Women's World Chess Championship 2006
Women's World Chess Championship 2008
IM Elisabeth Pähtz defeated WGM Ilaha Kadimova 4-3 in round one. Pähtz had white 1-0.
GM Monika Soćko defeated WGM Sabina-Francesca Foisor 4-3 in round one. Soćko had white 1-0.
Women's World Chess Championship 2010
Then IM Harika Dronavalli defeated then IM Mariya Muzychuk 4-3 in round three. Harika had black 0-1 (on time in a lost position!).
Women's World Chess Championship 2012
This was the first year of the extended tiebreaker with the rapid 10+10 games added.
Then IM Mariya Muzychuk defeated WGM Cristina Adela Foișor 4.5-4.5. Muzychuk had black ½-½.
Women's World Chess Championship 2015
GM Tatiana Kosintseva defeated WGM Mary Ann Gomes 5-4 in round one. Kosintseva had black 0-1.
Then WGM Aleksandra Goryachkina defeated IM Lilit Mkrtchian 5-4 in round one. Goryachkina had white 1-0.
Women's World Chess Championship 2017
IM Anastasia Bodnaruk defeated WGM Mitra Hejazipour 5-4 in round one. Bodnaruk had white 1-0.
GM Tan Zhongyi defeated GM Anna Ushenina 4.5-4.5 in round two. Zhongyi had black ½-½.
IM Nino Khurtsidze defeated then IM Nino Batsiashvili 5-4 in round two. Khurtsidze had black 0-1.
GM Tan Zhongyi defeated GM Harika Dronavalli 5-4 in the semi-finals. Tan had black 0-1.
Women's World Chess Championship 2018
GM Kateryna Lagno defeated WGM Natalia Pogonina 5-4 in round three. Lagno had white 1-0.
US Women’s Championship 2008
Then IM Anna Zatonskih defeated IM Irina Krush 3-2. Zatonskih was black, and white flagged, 0-1.
World Chess Armageddon Series 2019
Nepomniachtchi -Karjakin 0-1