I don't think so. If you're trying to debug some timing issue, then syslog may not be the right way to do that. However, if you're writing your own code, then you could include the time in the message portion of a
syslog(3C) call (or from the shell,
logger(1)). The log entry would still be on the whole second, but the message would contain the fractional part (although precision probably wouldn't be great if you're doing it from a shell script).
Maybe something along the lines of this:
// use gettimeofday(3C) to get microseconds (availability is hardware dependent)
syslog(LOG_INFO|LOG_LOCAL0, "Program foo timestamp: %d", microseconds);