He probably read them at some point
There is some evidence to suggest that Yudkowsky finished reading the original books sometime before he finished writing Harry Potter and the Methods of Rationality.
In the author's note at the beginning of chapter 96, he writes:
For those who have not read canon: The wooden sign has somewhat changed, but the inscription here is the same as in J.K. Rowling's original.
This quote implies, but does not prove, that Yudkowsky had finished reading the original series by the time he wrote this chapter. (The sign and its inscription are from Harry Potter and the Deathly Hallows, the final book of the series; if Yudkowsky had read Deathly Hallows, he had probably also read the prior books.)
Of course, it's possible Yudkowsky found the quote online rather than through reading the book. Interestingly, the inscription in Yudkowsky's version is not actually the same as in J.K. Rowling's original:
On this spot, on the night of 31 October 1981, Lily and James Potter lost their lives. Their son, Harry, remains the only wizard ever to have survived the Killing Curse. This house, invisible to Muggles, has been left in its ruined state as a monument to the Potters and as a reminder of the violence that tore apart their family.
- Harry Potter and the Deathly Hallows, chapter 17: "Bathilda's Secret"
On this spot, on the night of 31 October 1981,
Lily and James Potter lost their lives.
They were survived by their son, Harry Potter,
the only wizard ever to withstand the Killing Curse,
the Boy-Who-Lived, who broke You-Know-Who's power.
This house has been left in its ruined state,
as a monument to the Potters,
as a reminder of their sacrifice.
- Harry Potter and the Methods of Rationality, chapter 96: "Roles, Pt 7"
Possibly Yudkowsky means that the first sentence is the same, and the rest of the inscription is the part that "has somewhat changed." The changes (making the wording more poetic, talking up Harry more, and dropping the reference to Muggles) fit the tone of the fanfic chapter, so I suspect they're intentional and not a result of referencing an inaccurate quote online.
There is also an author's note on chapter 4 that references the original books:
As others have noted, the novels seem inconsistent in the apparent purchasing power of a Galleon; I'm picking a consistent value and sticking with it.
This could be read two ways: "Based on my reading, I think--and others agree--that the novels are inconsistent"; or "Other fanfiction authors have said--and I believe them--that the novels are inconsistent." I think the first interpretation is more likely; if that is the case, Yudkowsky would have read at least some of the original books by a very early point in the writing of HPMOR.