Within your home on the same network? No. You'll be limited by the slowest component, which is likely to be the wireless network. A common 802.11g WLAN operating at 54 megabits per second has a theoretical max transfer rate of 6.75 megabytes per second. At that speed 1 terabyte will take 1.8 days to transfer. Wireless overhead will typically make it take 20-25% longer.
If you change to standard 100 megabit LAN (wired) you will get 12.5 megabytes per second, which is about 24 hours theoretically. Wired overhead is about 10%.
If you use 802.11n, you can get a little over 100 megabit speeds, typically, but overhead and the nature of wireless will still cause it to take longer than than wired LAN.
If you change to 1 gigabit LAN (wired) you will get 125 megabytes per second, and your transfer will complete in about 2.5 hours, but at these speeds you're likely to hit the memory cache limits of your computer and transfer limits of your disks. Wired overhead is about 10%.
If you change to 10 gigabit LAN (not available on consumer grade equipment) you could get 1250 megabytes per second, and a 1 terabyte transfer would take about 14 minutes. At these speeds you will need a dedicated disk array to keep up with the network connection.