Business plan on their WordPress hosting servers can handle around 7,000 to 10,000 daily visitors but in terms of concurrent connections, it can handle up to 25 concurrent connections at once on the site/database. Usually to reach the 25 concurrent connection limit though would mean a couple hundred visitors can be on the site at once.
Hence, database connections open and close very fast so the site can still handle around 7,000 daily visitors a day but if the site is not optimized correctly, then the database connections cannot open and close fast enough which then can affect the amount of visitors you can get, but when using WordPress there are plugins to use to help with optimizing the site.
The amount of simultaneous visitors can vary depending on how your site is built and how fast those database connections open and close so there is not an amount of real time visitors I can provide unfortunately. It could be just 100 or up to even 300 depending on how your site is optimized.
If your website gets a high amount of traffic where you would need to be able to have more than 25 concurrent connections allowed on the site, then there are options to upgrade to a VPS or Dedicated server since those plans give you root server access which allows raising that connection limit to handle more traffic.
Their Optimized WordPress packages are subject to their Acceptable Use Policy (found here: https://www.hostgator.com/tos/acceptable-use-policy ) states that the package may not use twenty-five percent (25%) or more of their system resources for longer than ninety (90) seconds at a time. Given that each WordPress site is different, it would be very difficult to determine how many real time, simultaneous connections it would take to bring the site down. It would also depend on the scripts being run on the site.