How quickly a site is going to open would depend not just on the Internet connection of the site visitor, but also on the online connectivity of the hosting machine in which the website is hosted and on the network infrastructure - routers, server network card, etc. Slow connection or hardware which is unable to cope with a high volume of incoming and outgoing traffic may have direct impact on the user experience of your website visitors and the functionality of your website due to the fact that people shall most likely see error messages that the website isn't available or it will take a very long time for your content to load. In case this kind of a thing occurs, it's unlikely that the site visitors will revisit your website. For this reason you should always check out the connectivity of any server that you obtain and not only the main hardware components like hard disk, cpu and physical memory.