On the contrary, five Spartans are present for this game, and we now from Halo: The Fall of Reach that only four have died prior to the Battle of Reach (which takes place right before Halo: Combat Evolved). We know from Halo: The Fall of Reach, as well, that one of those four is Sam in 2525 over Chi Ceti IV, so we know that he isn't among the five on Harvest. We then know from Halo: Ghosts of Onyx that another of those four is Shiela, who died in 2544 over Miridem, so she wasn't part of the five. And we also know from Halo: Ghosts of Onyx that Kurt was actually kidnapped in 2531 in the Groombridge 34 System near a decomissioned refit station, so he isn't among the five either. We also know from Halo: Ghosts of Onyx that the fourth Spartan, Randall, is actually MIA, and that he died under mysterious circumstances. So he might be among the five, but it isn't very likely. So, we know that at the very least, four Spartans survive Reach, and if we were to assume that three of those Spartans were Grey Team and never worked with other Spartans again, that means one still gets back to the rest of the Spartans and, at the very least, tells John about this no xenomorphic alien that could very well threaten the universe at large. And, from there, John arrives at Installation 04 and is not entirely surprised by the Flood. Oh wait, that didn't happen. Sorry, I forgot, Halo Wars threw out canon so they could provide a "full Halo experience." The game, as an RTS on console, is amazing. As a Halo game, it is clear ES didn't know anything about the universe, and didn't spend much time or effort on getting it right. So yes, the Flood are in campaign, and no, it doesn't make any sense. If the five Spartans so much as hear about the Flood at some point in campaign, Halo Wars falls out of canon. But, judging from quotes on the new official Halo Wars site, I'm guessing that they'll probably just kill two or possibly more Spartans and fall out of much more definitive canon instead. I mean, heck, they already gave Spartans shields 21 years before they existed. Even says it in the game manual. Spartans have shields, and that is just the start of the crumbling of the continuity that made Halo such a fun story to follow.
I like pi.