Rod,
While SMTP is more reliable you can use PHP mail() for your list email. Do take care not to reduce the delays too much, as sending processes will increase with delayed DNS lookups, which are inevitable. Eventually, you could reach a server limit and start losing emails. SMTP uses a single connection for a large amount of email, greatly reducing load on the server. I don't see why they would block access to SMTP... Any user on the system can use many different methods to send email... Some examples utilizing system utilities via PHP or Perl, using PHP or Perl to ACT as an SMTP server (almost all hosts allow the connections required to do this), etc.
As long as they enable SMTP authorization and accept email from the local server (only paid users can access the local server) they should have no problems unless a user is abusing their service.
Please let me know if I can be of further guidance!
Regards