How quickly a site will open would depend not just on the Internet connection of the website visitor, but also on the connection of the hosting server in which the website is hosted and on the network infrastructure - routers, server network card, etcetera. Slow connection or hardware which can't handle a high volume of incoming and outgoing traffic could have direct impact on the user experience of your customers and the functionality of your internet site because people shall most likely see error messages that the internet site is not available or it will take some time for your content to load. In case this kind of a thing takes place, it is not likely that the site visitors will revisit the website. For this reason you have to always check the connectivity of any hosting server that you buy and not only the main hardware components which include hard drive, cpu and physical memory.