Should I purchase a 1080p Logitech webcam for low-speed internet?

I want a hugh quality camera for skyping. My friend said his connection can't take HD video on skype My Toshiba webcam is just terrible quality


http://www.amazon.com/Logitech-Webcam-Widescreen-Calling-Recording/dp/B006JH8T3S/ref=sr_1_1?s=electronics&ie=UTF8&qid=1387756156&sr=1-1&keywords=Logitech+HD+Pro