I have never seen a limit on the use of sendmail, other than what you agreed to in the TOS and what the maximum resource limits are on your account. I wouldn't try to send out 1000 emails at once, maybe break it up into groups of 10 every 5 minutes (the shortest interval using CRON) or every couple of page loads (using PHP).
Also, you must not use your account to send unsolicited emails. I would recommend doing a few things to not end up on the list of spammers:
1. Opt-in registration. Users must sign up to receive emails.
2. Confirmation. Send a confirmation before adding the user to the list of receivers.
3. Opt-out easily. Put a link in every email (at the bottom) and on your site so that users can easily choose to stop receiving your emails.
Hope this helps!