The Internet connection cannot actually make your computers slow down, but if most of what you do uses the Internet, such as browsing the web with Chrome or Internet Explorer, or even sending and receiving e-mail, then your computer will appear to be slow as those activities will be really slow because satellite Internet access is painfully slow. However, if you're just creating documents with Microsoft Excel or Word, then no, your Internet connection, no matter how slow, will not affect those local activities.