Intelligent reflecting surface (IRS) is a promising technology to improve the performance of wireless powered communication networks (WPCNs) due to its capability to reconfigure signal propagation environments via smart reflection. In particular, the high passive beamforming gain promised by IRS can significantly enhance the efficiency of both downlink wireless power transfer (DL WPT) and uplink wireless information transmission (UL WIT) in WPCNs. Although adopting different IRS phase shifts for DL WPT and UL WIT, i.e., dynamic IRS beamforming, is in principle possible but incurs additional signaling overhead and computational complexity, it is an open problem whether it is actually beneficial. To answer this question, we consider an IRS-assisted WPCN where multiple devices employ a hybrid access point (HAP) to first harvest energy and then transmit information using non-orthogonal multiple access (NOMA). Specifically, we aim to maximize the sum throughput of all devices by jointly optimizing the IRS phase shifts and the resource allocation. To this end, we first prove that dynamic IRS beamforming is not needed for the considered system, which helps reduce the number of IRS phase shifts to be optimized. Then, we propose both joint and alternating optimization based algorithms to solve the resulting problem. Simulation results demonstrate the effectiveness of our proposed designs over benchmark schemes and also provide useful insights into the importance of IRS for realizing spectrally and energy efficient WPCNs.