Have you looked at GZipWebClient? the bulk of the work is in the Zlib implementation and the client itself is just basically overriding the internal WebRequest/WebResponse.
You could likely get away with WebClient but restsharp goes much deeper. If it were my undertaking, I'd match it tit for tat and use request/response instead. The problem with that is it is pretty extensive to create a 1:1 branch of everything using 2 possible outcomes. Luckily you don't really have to as Morten just overrides the base classes and only does decompression if the gzip header is present. You would just have to understand the added layer if you wanted to inspect the code as you wouldn't be looking at the "traditional" request/response directly but that's hardly a reason not to include it.
Considering the Zlib code is ripped from DotNetZip which has mono support, it should "just work" on the mono side of things. Of course I'm not too aware of all the clients supported like monodroid but hopefully it wouldn't introduce too much of a headache. It's almost amazing to wonder why this wasn't included as part of the core framework on all CLR platforms a while back.