I imaging if you owned noreply.com you'd get a hefty amount of private correspondence in as well. I bet there are plenty of services out there that use noreply@noreply.com thinking it's the email equivalent of /dev/null for some magical reason.
I wrote an article a while back on this topic and whether the owners of test.com, check the email account test@test.com.
Didn't get a good answer but I would imagine they could see a lot of very personal information come their way as many geeks I've known use that to test their software.
Best practice as I understand it is to use emails that have the TLD "invalid", or one of a couple of others that have been explicitly set aside as "never will be issued" by RFCs. They also have the advantage of looking very out-of-place, where @test.com may slip by.
For testing, I usually use test{n}@testname.test. I've so far managed to avoid no-reply. If someone tries to reply to one of our message emails, I want to know what problem they're having, and the context to go with it from what message we sent them. "noreply" emails are anti-user-friendly.