While Business Class is called first, Business class always gets priority check in no matter when you show up. There will be a podium with Coach check in on the right side and Business Class check in on the left side. There will be a possibly long line leading to the right of the podium, and a short or non-existent line leading to the left side. The agent will serve the Business Class passenger pretty much before the next Coach passenger up when you step up to the podium.
Once past check in, there is one line leading around the corner to US Immigration (It is a two-step process. Customs is still done at the border in Blaine, WA in US territory).
I've taken the afternoon train regularly for years, the morning train is the same process.