logging.handlers.SysLogHandler in __init__ contains the following code, where socket is created and then connected right away. This seem to provide no way to specify a connection timeout for the socket being created.

sock = socket.socket(af, socktype, proto)
if socktype == socket.SOCK_STREAM:
    sock.connect(sa)

I believe to add an argument to specify the optional timeout would be appreciated, i.e., optionally calling sock.settimeout(..), something like:

sock = socket.socket(af, socktype, proto)
if timeout:
    sock.settimeout(timeout)
if socktype == socket.SOCK_STREAM:
    sock.connect(sa)