Can an SSB forward it's own OS and Weblogs? (4256592)

All of the SSB OS logs are stored under the built in source "local". You can configure the SSB OS logs to be forwarded to another destination under Log -> Paths in the SSB.

You could create a new path and select local under Source and your collection server under Destination. You will want to ensure that the "final" flag for the default path is unchecked. The following screenshot demonstrates this.

Regarding Web logs, at current there isn't a feature in SSB  to forward them to another destination.
Weblogs are located in this directory on the SSB : /var/log/lighttpd