Can we configure Apache to send logs directly to a log analysis system

You just specify ErrorLog and CustomLog within each VirtualHost directive. With that in mind, you would not be able to use ServerAlias and have separate log files for each host via normal performance without specifying separate VirtualHost.

However, you could pipe the log through a script, and have the script make the separate files. Look at the piped logging documentation.

You could also use a post processing script, such as utilizing grep to parse out the logs. A post processing script could be specified in the nightly logrotate under the postrotate or preprotate sections.

Apache 2.2 Piped Logging

Try sending all of ErrorLog to a pipe, for example a perl script. This perl script could direct to syslog and the local disk.