Not necessarily. First of all: You can't put in a gigabyte card in your Xbox. The Xbox has an on-board ethernet port, that is not exchangeable.
Since the game programmers know, that the Internet is a comparably slow transfer medium, they optimize their networking code for slow connections.
And since most Internet connections for private users don't exceed 50 or 100 megabit / sec (for fibre and VDSL connections), there is no real use for gigabit networks in the Xbox.
Also: Depending on the cable connection, you won't also see big improvements with lag.
Most Xbox games are peer to peer network games. This means, even if you have a blazingly fast connection - if there are players with slow connections, they will lag on your fibre connection the same as with your current cable.
Switching to Fibre will however make marketplace downloads faster for you, improve the lag of your movements fo *other* players with a faster connection than yours, and you will be able to enjoy 1080p movies from the upcoming Zune Videomarketplace.
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