Thanks to everyone for your feedback.
Just an update on this. We did a test with about 40 people each submitting 10 assignments within a half-hour period on our test server which does not have very much hardware (two web servers each with 2 CPUs). Each assignment file was about 10MB.
Moodle coped very well apart from one thing. Uploading files was slow, because after each file had been sent to the server, there was a long wait while ClamAV ran. You could see this in the file-picker. If you dragged in a file, the green progress bar would get to 100% quite quickly, but there would then be a ~1minute delay before the upload completed and the file was shown if the file manager.
Obviously, MDL-50886 is going to help with this. (Thanks Ruslan and Lancaster University.)
Also, it would be nice to have some sort of 'Virus checking' progress message after the progress bar has got to 100% so people know what is going on.
If anyone else has any thoughts about this, please let me know. Thanks.