That iMac has two Thunderbolt 1 ports that have Mini DisplayPort connectors and can double as Mini DisplayPorts.
Apple says that it "Simultaneously supports full native resolution on the built-in display and up to a 30-inch display (2560 by 1600 pixels) on an external display."
iMac (27-inch, Late 2013) - Technical Specifications
You're asking about some "USB 3.0 to HDMI / VGA Adapter 1920 * 1080 Dual Display Converter". I don't know how well that would work, if it would work, or whether it might require the installation of some special driver. Those USB adapters (note: this is an old USB-A adapter, not a USB-C (DisplayPort) one) are what people sometimes turned to when they didn't have "proper" video outputs.
If you're trying to connect one external monitor, you'd be much better off using the Mac's built-in Mini DisplayPort video output. You can get adapters to take that to full-size DisplayPort, HDMI, or VGA, if needed.