Actually, there is.

http://www.avast.com/eng/test-url-blocker.html This tests the Network Shield scanner in real-time. As this is only a test file, it is similar to EICAR.

EICAR is designed more for static scanning similar to using File System Shield when running a manual scan of the hard drive.

[EDIT:] Thanks to Asyn for providing the url test file some time ago. I’ve bookmarked the resulting page in my browser and sometimes use that to check for proper operation that way. See attached below to see what to expect.