How quickly a site is going to open would depend not only on the Internet connection of the website visitor, but also on the connection of the hosting machine where the website is hosted and on the network infrastructure - routers, server network card, and so forth. Slow connection or hardware that can't deal with a high volume of incoming and outbound traffic may have direct impact on the user experience of your visitors and the functionality of your site as people shall most likely see error messages that the website is not available or it will take some time for your content to load. In the event that this kind of a thing occurs, it's unlikely that the visitors shall revisit your website. For that reason you should always examine the connectivity of any server that you obtain and not just the main hardware components which include hard disk, processor and physical memory.