Based on the community answer, yes: the TG-series camera can charge over USB, so the Olympus-supplied unit is effectively acting as a USB power adapter.

That means a normal modern USB charger should also work, as long as it provides the correct USB power output. The Olympus adapter may differ mainly in physical design, branding, or regional plug format rather than in any unique charging function.

As with most cameras, the actual battery charging control is typically handled by the camera when connected over USB, not by a “smart” wall brick. Manufacturers often recommend only their own accessory, but in this case the evidence provided indicates standard USB charging is supported.

For safest use, stick to a reputable 5V USB charger and proper cable.