Occasionally they will actually read short passages from readers. After they read anything they will have to fill in some sort of (standards aligned) paperwork. They will never have extended reading time in class.
As an example, a 1st grade reading teacher needs to cover CCSS.ELA-LITERACY.RL.1.(1-10) (reading literature); CCSS.ELA-LITERACY.RI.1.(1-10) (reading information text); and CCSS.ELA-LITERACY.RF.1.(1-4) (but actually 15 substandards) (foundational skills).
Actual standards at http://www.corestandards.org/ELA-Literacy/RF/1/