It must have a positive impact, I am now able to access the server using HTTP, but not using HTTPS.
nginx is running on my raspberry, port 80 for http, for 443 for https. External ports are routed to according internal ports.

So HTTP is fine, HTTPS still returns an ERR_TUNNEL_CONNECTION_FAILED from my work computer. But from my phone, it works fine.
Error log is:
2015/04/23 15:04:04 [error] 2151#0: *8964 upstream prematurely closed connection while reading response header from upstream, client: 109.99.99.99 , server: , request: "GET /socket.io/?EIO=3&transport=polling&t=1429794125290-15&sid=ZjXxkYkMXrbfNkTbAACm HTTP/1.1", upstream: "http://127.0.0.1:8070/socket.io/?EIO=3&transport=polling&t=1429794125290-15&sid=ZjXxkYkMXrbfNkTbAACm", host: "truc:4321", referrer: "https://truc:4321/jeedom/index.php?v=m&"

Something that could help, maybe: I notice that referrer is a hostname, some for host, but I am accessing with an ip address. Is it expected ?