Yes, the ports use emscripten to convert to JavaScript/asm.js.
http://blogs.unity3d.com/2014/10/07/benchmarking-unity-perfo...
It does run somewhat slower in a browser compared to native, but the difference is really not very big.
To put it another way, the differences between browsers are about the same size as the difference between the fastest browser and native. So it's in the right ballpark.
1: https://developer.mozilla.org/en-US/demos/detail/bananabread