Yes most definitely. You can get quite a respectable computer for that right now. But I would like to warn you away from buying either Alienware or Dells high end series, you will be paying a considerable amount more for what you are getting than from other vendors.
Personally, I recommend either the
G75VW series from Asus (here is the
websites page), I have had a number of friends own past and current laptops from this series and they have proved to both be powerful and reliable.
As a side note, I would strongly recommend you choose Windows 7 as your OS for now, and that if you do not already have a high DPI(4000-6000 DPI) mouse, I recommend you get one . The reason for Windows 7, is that currently it is Microsoft's tick, so it is more reliable and most games are being geared towards that still. The mouse, is because playing with a track pad is terrible, and software acceleration for mice is rather common and makes moving through a game or any UI for that matter like steering a large boat, your turns are slow and not precise.
Lastly, as a quick comparison here is the popular
Alienware outfitted to the same specs, and
IBuyPower with a similar configuration.