It is possible. The config file is just an XML text file. We created a 'master' minimal config that then gets copied to each server after the forwarder app is installed. One issue is that if the device does not have the event logs that are configured the Solarwinds forwarder app will not start. For that reason our master config only includes Windows default event logs, no installed application event logs.
You can do similar installs with the syslog server but it still requires manual steps. Install a syslog server, configure your rules, and export the config. On the new server, install Kiwi syslog server and create any paths required by the config. Import the config and restart the service.
We also run multiple instance with few in HA as well. We do similar to what kstone mentioned. Create a standard set and copy it over to multiple servers and do an import. If you copy the file in syslogd folder then it will pick it directly while starting of the application.