Yes, you can use the Hudson Remote API for this (as @Dan mentioned). Specifically, you need to configure your job to accept Remote Triggers (Job Configuration -> Build Triggers -> Trigger builds remotely) and then you can fire off a build with a simple HTTP GET to the right url.
(You may need to jump through a couple additional hoops if your Hudson requires authentication.)
I'm able to start a Hudson job with wget:
wget --auth-no-challenge --http-user=test --http-password=test "http://localhost:8080/job/My job/build?TOKEN=test"
This returns a bunch of HTML with a build number #20
that you could parse. The build number can then be used to query whether the job is done / successful.
You can examine the Hudson Remote API right from your browser for most of the Hudson web pages that you normally access by appending /api
(or /api/xml
to see the actual XML output), e.g. http://your-hudson/job/My job/api/
.
Update: I see from your question that you probably know much of what I wrote. It is worth exploring the built-in Hudson API documentation a bit. I just discovered this tidbit that might help.
You can get the build number of the latest build (as plain text) from the URL: http://your-hudson/job/My job/lastBuild/buildNumber
Once you have the build number, I think the polling and job status is straightforward once you understand the API.