Generally speaking, yes a faster connection will download a webpage quicker than a slow connections. But in reality, there are a lot of things that will affect how fast you can download and display a webpage:
Even if you have a download speed of 1 Gbit/s (Google Fiber), if the server you are retrieving information from only has an upload speed of 56 Kbit/s (Dial-up), you're only going to get your webpage at 56 Kbit/s. Your download speed is only as fast as the slowest part in the chain.
- Type of connection to your ISP
With some ISPs, they say you will get "up to" 1 Gbit/s but if they have it set up where they share that connection with 100 different users, you may be getting a lot slower speed than what you think you are. In the middle of the night when no one is on the shared internet, you may be getting those speeds but in the evening when everyone is streaming Netflix, it will be a lot slower.
Depending on how long it takes for your request to reach the server also determines how long it will take for you to get your webpage. If your friend's connection allows him to send a request in 1 ms and your connection takes 500 ms, he'll be getting the webpage 499 ms faster than you will.
With most modern computers, they can display a webpage faster than it takes to actually download the page itself. But if you have a 5 year old laptop that happens to be running a virus check in the background and has 50 different tabs open, it'll usually take a lot longer than a new computer with a fresh install of Windows with nothing else happening on the computer.
Finally, Which browser you use also determines how quickly you will be able to view a webpage. Browsers like Chrome and Firefox are usually quicker at displaying webpages than IE is, but there are certain webpages that IE will display quicker.