Carol's thing with microbes IMHO falls closer to the "passion" than "pressure" end of the scale, as she's the "clean" one, not tempted to cheat despite being the formal project leader.
And it's strongly implied that David knew more about the actual nuts and bolts of the project than his mother did. Genesis was David's chance to make a name for himself, but his mother was already an accomplished scientist who probably oversaw the project because her name and reputation (before TWOK) gave the project credibility it otherwise wouldn't have had.
Indeed, the Myriad Universe
novel "The Chimes at Midnight" actually states that David conceived the Genesis Wave himself by running a series of computer simulations while helping his mother work at an Andorian research lab: this material isn't cannon, however. The story's main protagonist isn't David or Kirk, but Thelin, the Andorian Starfleet Officer who became Kirk's closest friend and executive officer in the reality where Spock was killed at the age of seven. The story depicts a fourteen-year-old Marcus running a complicated computer simulation when a picture of the Genesis Wave suddenly appears on his computer monitor, drawing the attention of the scientists working in the lab.
The story comes full circle later when Thelin works with David to protect the Enterprise
from the Genesis blast radius: in the story, Thelin doesn't sacrifice himself as Spock did but devises a method of preventing the ship from being absorbed when Reliant
explodes, relying on knowledge he gained watching David run the computer simulation several years earlier, as he was in the same laboratory at the time. But I digress...
Whether Carol knew about David's actions in using the proto-matter isn't clear (I'm inclined to think she didn't know), but as the official face of the endeavor, it would not have served her best interests to cut corners with any aspect of the project. Such feelings could easily manifest in her comments to Terrell.
It's too bad there was never a conversation between Saavik and Carol on screen after TSFS. Kirk may have known what David did ("I went wrong," "Genesis doesn't work"), but there's no way to know if he told Carol.