Is it possible to do an asynchronous build of a unity player?
I’ve scoured the docs but not found anything, am I missing something?
This is not possible, I’m afraid, and for good reason. 
What if you changed anything while the project was building, like editing a script so it no longer compiled? Tons of stuff could go wrong. :-/
The closest you can get to asynchronous building is to have a build server with Continuous Integration (like Team City) running on a separate machine, and then hook that up to SVN so that it performs a new build every time you do a commit. We have a setup like that going on in our team, but I can’t tell you the specifics about its installation as it was done by another team member - This is just to inform you that it’s possible, and that it will do builds on a separate server, which I guess makes it asynchronous to your machine.
If you’re interested, search keywords would be things like “Team City”, “MSBuild”, “SVN” and the page on command line arguments for making the editor produce a build.
It’s possible to build in the background on the same computer (and even do multiple builds at once), you just need to copy your project tree to a temp directory for each build via a batch file or shell script. More info here.