I'd like to be able to check which version of server (RTC and RQM) I'm
running, from within a shell script. Is it safe to run repotools.sh
and use the version number from the first line of the output, or will
this only tell me which version of repotools I'm using?

I believe it is the repotools version.
Maybe you could use curl to fetch the information from the server. The
following URL provides the version among other things:

https://<server>/jazz/service/com.ibm.team.repository.service.internal.IServerStatusRestService/serverInfo

If you have to deal with form based authentication, you can log in using
curl as well:

COOKIES=./cookies.txt
HOST=https://localhost:9443/jazz
....
curl -k -c $COOKIES -d j_username=$USER -d j_password=$PWD
$HOST/j_security_check

--
Regards,
Patrick
Jazz Work Item Team