It is technically possible but the IPC will destroy you. You would need to transfer inputs and outputs as well as have JS shims to call it. Most of the code will be doing tons of memory accesses which will need to be transferred back and forth across the process boundary and orders of magnitude more cost.
If you did want to try the best approach is probably to compile Dolphin to WASM and render via WebGPU. Then you can JIT WASM. But I suspect that the overall performance will still be lower. (Although a web version of Dolphin would still be super cool.)
I don't think it would be as simple as compiling Dolphin to WASM. Since Dolphin itself implements a JIT compiler that emits native code you would need to also teach Dolphin to emit WASM code.
If you did want to try the best approach is probably to compile Dolphin to WASM and render via WebGPU. Then you can JIT WASM. But I suspect that the overall performance will still be lower. (Although a web version of Dolphin would still be super cool.)