There is a dangerous way to do this. You can use the CISCO-CONFIG-COPY-MIB to copy a "do" command into the running-config which will trigger a TFTP transfer of the show command output. See http://www.cisco.com/en/US/tech/tk648/tk362/technologies_configuration_example09186a0080094aa6.shtml on how to use the CISCO-CONFIG-COPY-MIB.
Your config snippet which will trigger the TFTP will be something like:
do show logg | redirect tftp://10.1.1.1/show_logg.txt
end
You will probably need to pre-create the show_logg.txt file on your TFTP server. The big caution with this approach is that any interactive command will cause SNMP and the config to lock up forcing a reload.