No issues. Once a server is correctly configured as a mail server (SMTP) for a particular domain, there is no difference if the mail it sends out came to it from Outlook, or from the mail()
function in PHP - both are getting the SMTP server to do all the heavy lifting
I always make sure to set my X-Mailer headers correctly (identifying that the message was sent from within PHP) to ensure that any overzealous anti-spam services recognize it as an automatated notification as opposed to bulk/junk email. e.g.
$headers .= "X-Mailer: PHP/".phpversion();
All the configuration and limits you'll encounter are with the SMTP server, not from PHP. You can configure SMTP to rate-limit to 2 messages per second for example, this means if you queue up 1,200 messages they'll be drip fed out over the next hour rather than all at once (two is a really low number, 5-25 is more realistic).
SMTP is the backbone of email and some SMTP servers can happily handle tens of thousands of messages per minute (or more!) - the only limitation you'll likely face is bandwdith ;)