2019 UPDATE: in GoDaddy documentation page there are new email limits per day and no more reference to the SMTP relay reported below, so probably it’s not needed anymore. Plase refer to the documentation on GoDaddy site.
You can not use an external SMTP. That’s all.
GoDaddy does not let connection on external SMTPs from shared hosting plan. If you want to configure an SMTP to send email (for example with Newsletter, but it’s not a Newsletter problem!) you can use their SMTP.
No connection to other SMTPs is allowed. That SMTP has a limit of 1000 email per day and, as I read on support forum, you must send email where the sender is an address within your domain (like firstname.lastname@example.org).
If you want to have more information: https://www.godaddy.com/help/hosting-email-relay-limits-27150.
If you do not use their SMTP service (but the standard mailing function of PHP – used by default from WordPress) the limit seems to be 250 email per day. I have not official confirms.
Just a note: my HostGator account allows me 500 emails per hour (if you want to signup with a discount use SATOLLONET as coupon code). DreamHost has a 100 to 200 emails per hour limit (you can use SATOLLONET discount code to have a 47$ discount).
I cited DreamHost and HostGator because I know them and I know they allow external SMTP connections. Other hosting provider are good as well.