I think the effect would be positive depending on the level of difficulty of the game. The attached conference paper sheds light on your topic that I hope would be helpful.
Many thanks,
Debra
Conference Paper Gamification of Introductory Psychology: Using an external a...
We use a full course integration gamification model at the school where I currently teach. The world we have crafted is based on the social studies content standards for the year and our days are turns based in that world.
The game is open-world, meaning students choose their own path (that hasn't been laid out before) based upon their knowledge of the society in which they have been placed. They work with the teacher to create plans for their character and can create subtle plans to create trade empires or even become the next king/emperor (if the history of the point has a coup or a similar overthrowing). They can do anything they can think up, as long as it flows with history and doesn't use technology or ideas ahead of the times. This creates real depth over time as students seek to understand many facets of the time and the technology available to them in order to build trade or conquer.
This year's 7th graders are working with Ancient Mesopotamian, Chinese, Indian, Mongolian, and African history. As we walk through the timeline of these civilizations, the students work to move up the social ladder of that civilization. At the teachers, we do no direct instruction and leave it to the students to find out information that could be beneficial to know for their character (or his/her decedents as we push further through history) during that time period. They may receive letters from dignitaries (if the job they have managed to get via research and posturing) that outline a new policy being advocated for in trade between nations they represent.
The students generatively use each class to deepen understanding so that they can use the knowledge to benefit their character. This includes learning the science and math necessary to figuring out whatever problem they are working on. If they want to trade silk to Mesopotamia, they need to figure out how silk was made ancient style, have the capital (or find a way to generate the capital) to buy the first generation of silk worms, plant and grow mulberry leaves (or find an orchard to buy from - controlled by the teacher as an npc), and then fund the process while they wait for it to become fruitful. They read articles, write correspondents to their families if away trading, and all around fulfill every standard they need by playing and interacting with the game.
Sorry for the novel, but the complexity of the autonomy and accountability necessitates some heavy explanation. I apologize if this is nowhere near what you wanted. Just thought I should share.
Maybe this article: "Meaningful Learning fostering For The Students' Pragmatic Competence", can answer your questions. Because in my opinion "deep learning" is Synonymous with "meaningful learning". The following articles can be downloaded: https://www.researchgate.net/publication/305912852_Meaningful_Learning_For_Fostering_The_Students%27_Pragmatic_Competence
Best Regards.
Conference Paper Meaningful Learning For Fostering The Students' Pragmatic Competence