No, that's not the case because you are mixing 2 different problems.
Syslog already allows for secure, autenticated and reliable network communications, particulary using the RELP protocol (rfc 3195), so ther's no need to add an overhead to that phase.
The hash is then added only when the message is saved on the disk, non before sending it over the network. It's scope is only to guarantee that the log has not been modified after being written, not to guarantee it's immutable during network paths.
A "continuous hashing" calculated on a per file basis (or per DB if you prefer to save data in a database) is a possible cheap solution to this problem.
The solution is not complete as a journal, but it's really really simple to add to existing daemons (rsyslog and syslog-ng), does not require any invasive operation on the syslog infrastructure, allows a complete backward compatibility and satisfy a big part of the problem addressed by journal in a simple.