Greetings,
On a dedicated high-end server you should be able to send as much email as you want, although I don't recommend more than about 150k per day per server). I do not believe HostGator's shared hosting policy (mentioned
here) would apply to dedicated servers.
A dedicated server can reasonably be expected to be used for commercial email marketing. If you send unprofessional email your server provider might take notice, but if you send professional email and always include a remove link, as well as have "signup forms" or lead sources so you can explain where you get your subscribers from, you should be allowed to send a very reasonable amount of email (Again I recommend ~150k/day max to be safe and so you can work on your reputation with the various providers such as Yahoo).
I am not familiar with any method to monitor PHP mail to make it more stable and do not have immediate plans to do so, however it does sound like a good suggestion to look into that.
Please let me know if you have any more questions!
Regards