We studied polycrystalline B2-type Co2FeAl (CFA) full-Heusler alloy based magnetic tunnel junctions (MTJs) fabricated on a Si/SiO2 amorphous substrate. Polycrystalline CFA films with a (001) orientation, a high B2 ordering, and a flat surface were achieved using a MgO buffer layer. A tunnel magnetoresistance (TMR) ratio up to 175% was obtained for an MTJ with a CFA/MgO/CoFe structure on a 7.5-nm-thick MgO buffer. Spin-transfer torque induced magnetization switching was achieved in the MTJs with a 2-nm-thick polycrystalline CFA film as a switching layer. Using a thermal activation model, the intrinsic critical current density (Jc0) was determined to be 8.2 x 10^6 A/cm^2, which is lower than 2.9 x 10^7 A/cm^2, the value for epitaxial CFA-MTJs [Appl. Phys. Lett. 100, 182403 (2012)]. We found that the Gilbert damping constant evaluated using ferromagnetic resonance measurements for the polycrystalline CFA film was ~0.015 and was almost independent of the CFA thickness (2~18 nm). The low Jc0 for the polycrystalline MTJ was mainly attributed to the low damping of the CFA layer compared with the value in the epitaxial one (~0.04).