Hi Matthew,
I was doing some research on this last night because it occurred to me as well.
The short answer is "mostly no". It's not something that servers support much.
If you did want to do it then you'd need to set the "content-encoding" header to Gzip.
Some servers might specifically check for the header, and knowing they don't support the feature at least give you back an error code. Other servers may just choke on the POST data completely.
I think it should be reasonably simple to add support to the NetTalk server though, and by extension to the NetTalk WebClient. Then at least if you were using a NetWebClient to talk to a NetWebServer you'd be able to take advantage of this. This might lead, slightly down the road, to compressing ajax requests from the browser as well - but we'll have to wait and see about that.
cheers
Bruce