Having taught piano at a Suzuki music school, and knowing many other Suzuki instructors of both piano and strings, it varies WIDELY as to when note reading is introduced. We always used Hal Leonard or a similar series for reading once the piano students were about half-way through the first piano book, but I once had a transfer student that moved from another city who was nearly done with book two Suzuki with almost no reading ability!
As I am currently going through a similar situation with a transfer Simply Music family (the 11 year old did that method for 5 years, the 7 year old for 1, and luckily they can at least read rhythms already), here is what I have been doing: playing a bit by ear/rote, "discovering" a particular reading concept (finding middle C/treble G/bass F, directional steps, skips, etc.), then using PA Primer and Level 1 books to reinforce the concepts by sight reading as much as possible through the rest of the lesson, stopping to answer questions as we go. I then have each student pick 1 or 2 of the sight-read pieces to practice over the week. So far this has been working rather well for both students. I am focusing more on the "guide notes" and directional reading for now, allowing them to move out of what is perceived as "baby" pieces a bit faster than simply having them name all notes as they go. We will fill in the remaining note names with time and practice.