Yes. The LM317/337 board you ordered can take AC or DC input. It has the rectifier, caps and the regulators. I would not use a SMPS.
Hardware: RPi Zero W | Allo Kali | ProtoDAC TDA1387 X8 | PGA2311 | Icepower 500ASP | Harbeth SHL5
Software: Moode 8.3.3
Source: Win 10 NAS
Software: Moode 8.3.3
Source: Win 10 NAS