There's no description of the time spent in "Stockers & Backgrounders" phase, but we can infer it. 18-22 months to cattle market weight, and 4-6 months at feedlots mean that they scarcely spend a few extra months there.

This paints a picture of indeed grazing on grass for majority of lifespan, albeit not an overwhelmingly large portion. Also that they are slaughtered at a surprisingly young age.