How quickly a website is going to 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, etc. Slow connection or hardware which cannot deal with a high volume of inbound and outbound traffic might have strong influence on the consumer experience of your customers and the performance of your site since people will most likely see error messages that the internet site isn't available or it shall take a very long time for your content to load. In case such a thing happens, it's unlikely that the website visitors shall return to the website. For this reason you must always examine the connectivity of any hosting server that you obtain and not only the main hardware components such as hard disk drive, central processing unit and physical memory.