I'd say yes, since there's great examples of it happening. Launch titles of course have an incredible track record. Super Mario World, Mario 64, Halo CE, Wii Sports (not a critical darling, but popular) and Breath of the Wild all primed their console for success, or at least turned a potential failure of a system into a potential contender.
But there's examples of it happening sometime after launch. There's no guarantees though, a lot has to come together for it to happen. The best time for a game to change a console's fortunes after launch is during a relaunch for a troubled system and when the majority of the sytem's lifespan is still in front of it. Sonic 2 and its bundle with the redesigned Genesis was so extremely successful that it turned the Genesis into a contender. Pokemon Diamond and Pearl along with the DS Lite revision turned that system around. Uncharted 2 and the PS3 Slim pretty much relaunched the PS3 and set Sony up for success later.
There's some rare examples of it happening late in a system's life. Pokemon Red and Blue gave the tired Game Boy additional years of life. The Last of Us helped the Playstation brand more than it helped the actual PS3, but it burnished Sony's reputation as the place for killer first-party titles between it and Xbox and that helped the PS4 immensely.
Other times though it's just simply way too late or not enough. The N64 had some incredibly heavy-hitting titles early enough in 1997 and 1998 like Goldeneye, Ocarina of Time, and Banjo-Kazooie, and while they sold systems and floated the N64's fortunes, they weren't enough to secure victory that generation. The N64 also had a very late lineup of heavy-hitters in Perfect Dark, Conker's Bad Fury Day, and Majora's Mask that were all way too late to matter. Resident Evil 4 and Twilight Princess also came very late in the Gamecube's life, and had they come out in say 2002 then maybe the Gamecube sells 40 million lifetime that generation. Halo 2 is interesting since it was too late and not enough for the Xbox, and Microsoft was going ahead with an early 360 launch anyway, but Halo 2 was the online killer app for the first two years of the 360's life, and that helped against the PS3.