3 metres is about 3 yards, right? around 30 feet.. most wireless routers (without the long range antennas) only work effectively 25-30 feet. But for gaming, You're going to have trouble getting a good connection that far away.
I know with My 360, We couldn't get further than 15 feet without it starting to lag out on us. (albeit we did use a Third Party Adapter) But Still, The 360 adapter uses the same tech.
I would say it'd be more worth it to you to run an ethernet cable under the baseboards and just bring it out near your 360 rather than have it going with wireless.