Setting option SO_SNDTIMEO to the socket cause connect() return with EINPROGRESS errno after timeout, but this nonstandard feature is not described in man pages of socket(7) and connect(2).

Sample:

int main(int argc, char *argv[])
{
    int sockfd, n;
    struct sockaddr_in serv_addr;

    struct timeval timeout;
    timeout.tv_sec = 4;
    timeout.tv_usec = 0;

    if( (sockfd = socket(AF_INET, SOCK_STREAM, 0)) == -1)
    {
        perror("socket");
        return -1;
    }

    if( setsockopt(sockfd, SOL_SOCKET, SO_SNDTIMEO, &timeout, sizeof(timeout)) == -1 )
    {
        perror("setsockopt");
        return -1;
    }

    bzero (&serv_addr, sizeof(serv_addr));
    serv_addr.sin_family = AF_INET;
    serv_addr.sin_port = htons(9999);

    if(inet_pton(AF_INET, argv[1], &serv_addr.sin_addr) < 1)
    {
        printf("Invalid IP address value. Exit.\n");
        return -1;
    }

    if(connect(sockfd, (struct sockaddr*) &serv_addr, sizeof(serv_addr)) < 0)
    {
        printf("errno = %d\n", errno);
        perror("connect()");
        return -1;
    }

    close(sockfd);

    return 0;
}

$ time ./client 88.88.88.88
errno = 115
connect(): Operation now in progress

real    0m4.001s
user    0m0.000s
sys     0m0.000s

# tcpdump -i ppp0 -n port 9999 -ttt
tcpdump: verbose output suppressed, use -v or -vv for full protocol decode
listening on ppp0, link-type LINUX_SLL (Linux cooked), capture size 96 bytes
000000 IP 81.25.50.166.47087 > 88.88.88.88.9999: S 3574453598:3574453598(0) win 5840 <mss 1460,sackOK,timestamp 207409345 0,nop,wscale 6>
2. 997721 IP 81.25.50.166.47087 > 88.88.88.88.9999: S 3574453598:3574453598(0) win 5840 <mss 1460,sackOK,timestamp 207410245 0,nop,wscale 6>