We're just making the transition to using WeBWorK for our placement exam for incoming freshmen here at the University of Michigan. That's not a calculus placement test, but our preliminary work suggests that the Gateway/Quiz assignment type in WeBWorK should work for the testing as we do it (that is, as an on-line, unproctored, but timed test). We have several thousand students who take the test, albeit over the course of the summer. We also have a pretty good server to manage the load.
For our test we don't want students to see their results, nor the problems, once they're done. This is something that I've added to the HEAD (unstable) branch of WeBWorK, but that should become stable soon and migrate out to the production branch.