I'm writing a program which is sending files through SMTP, thanks to my (local) Postfix server, on port 25.
Is it possible to use several threads (thus several sockets) to inject emails faster ?
Depends entirely on where the bottleneck is.  If it's on the SMTP server or the network, the answer is no.  If it's in your python code, probably yes.
Several threads connecting to a Postfix server?