Yes, it is possible. But you should do not do it if your only reason is rejecting learning new technologies.
For now (using Qt 5.14), Qt for WebAssembly is deployed as an official platform.
Unfortunately, it is young platform support with a lot of problems and possible future changes.
You should know Qt for WebAssembly does support all Qt modules. See Supported Qt Modules.
Qt for WebAssembly was created for the purpose of port one code base in other platform (it is generally Qt develop way, please see Qt for MCU). With other technologies in this stack, like QRemoteObject, are very interesting technologies. It was not created for websites in a normal network.
The main Qt for WebAssembly target are internal network systems and remote control of devices. Pay attention to this.
Unfortunately, not all browsers will support WebAssembly. See Qt for WebAssembly support notes.
Additionally, in Qt, you can't find a built-in rest-API handle or other standard web technologies to integrate with your existing backed.