Your SMTP server (I assume you are using SMTP) will simply make a TCP connection to the remote SMTP server once it has resolved the DNS address. Once the connection is made it will transmit the message.
However, during the transmission you will be sending information across the internet which means the information will likely go to your ISP and then through a backbone to the destination ISP as part of the normal routing process. There is no additional routing or communication with external machines as part of SMTP.
Any of these middle services (most likely your ISP or their ISP) may complain about excessive data transfers if it violates any contract you may have.
Also, the destination SMTP server could very well blacklist you if they don't appreciate the large volume of mail.
However, if you owned both SMTP servers and had a normal contract with your ISP you shouldn't be blacklisted for this as you won't be accessing any other servers as part of the SMTP process.