The main server at our organisation is still running SME 5.6, so for obvious reasons I'd like to upgrade it to 6.0.1. The only problem is that we migrated our email from the original UW-IMAP to Courier (v 1.6.1-2) a few years ago, using a contrib. Does the upgrade process handle this...
I'd guess not. You're probably better to target your migration to 7.0 than 6.0.1. The mailbox layout in 7.0 is closer to courier than 6.x is, and 6.x doesn't match the standard dovecot layout either.
, or will I have to migrate things manually? (e.g. using the courier2dovecot script at http://bendiken.net/scripts/ )
That might be useful. But it looks like the main things that could be missing without that script is mailbox subscription lists, and you'd invalidate client caches of message metadata. Neither of those is likely to be catastrophic.
And is it advisable to remove Courier before upgrading, or should I leave it?
You should remove it.
And I have more or less the same question about Jesper Knudsen's ClamAV (v 0.70) sme-antivirus contrib/script for SME 5.6 ( http://sme.swerts-knudsen.dk/ ) that I installed back in 2003. Is it OK to leave that, or will it cause trouble later?
Unless someone has assured you that a contrib will behave sanely when you upgrade then you should remove it before upgrading. Jesper's contrib will probably be OK during upgrade to 6.x, but will probably be troublesome during an upgrade to 7 (since 7 includes antivirus capabilities).