Hostgator hosting permit up to a 200 email sending per hour per domain. If you send over this amount in any hour, most of the e-mails will bounce back with a undeliverable error. That makes 4800 emails daily limit. Honestly speaking, that is a huge amount, compare to godaddy host that allow 250 in total per day per domain. So, guess what the value for money at hostgator.
For user that require mailing sending larger than 5,000, you can setup a semi-dedicated or dedicated hosting solution from hostgator. Thus solve all your problem. An email system for all size of website 