There is no limitation to the number of outgoing connections besides the following:
1.) The file descriptor (fd) limit which is imposed by the kernel itself (via ulimit) on Syslog-ng, however, this can be adjusted by changing the ulimits on the kernel.
2.) The /proc/sys/fs/file-max kernel tunable, which is an unsigned long value, allowing a theoretical maximum of 4.2 billion open files on a system.
Other than those 2 limitations, Syslog-ng has no maximum number of outgoing TCP connections that can be made.