How quickly a site shall open would depend not just on the Internet connection of the site visitor, but also on the connection of the hosting server in which the site is hosted and on the network infrastructure - routers, server network card, etc. Slow connection or hardware that can't handle a high volume of inbound and outbound traffic can have direct influence on the consumer experience of your visitors and the functionality of your website since people will most likely see error messages that the website isn't available or it shall take some time for your content to load. In the event that this sort of a thing happens, it is not very likely that the visitors shall return to the website. For this reason you have to always confirm the connectivity of any hosting machine that you purchase and not just the main hardware components like hard drive, central processing unit and physical memory.