Depends on your definition of "works."
The Neewer TT560/Godox TT560/Amazon Basics flash is a single-pin manual only flash. It cannot do TTL, HSS, or talk to your camera's flash menus. All you can tell this flash to do via the single pin on its foot is tell it when to fire. And that should work on an Olympus camera hotshoe or with radio triggers. But that's all you can tell it to do.
Flash can be more transformative to your photography than a lens. Budgeting accordingly isn't stupid. Particularly for a first/only speedlight, which you may want to use for on-camera run'n'gun shooting in TTL, as well as off-camera "Strobist" setups. I'd highly recommend you consider getting a TT685-O and a Godox 2.4 GHz "-O" transmitter for Olympus/Panasonic, instead. That way, you'd have TTL, HSS, and power control both on and off the camera hotshoe.