Usually, processors themselves never are the big deal when it comes to whether Linux can run on it. The most affected hardware parts are graphics cards/chips.
The Graphics you name work with the proprietary nVidia driver. To do this, open the Software & Updates utility, go to the Additional drivers tab and select nvidia-331 for your graphics card, then reboot.
A faster option would be to run the command sudo apt-get install nvidia-common nvidia-331
from a terminal, then reboot. This also works, if you're unable to use Ubuntu with a graphical frontend due to a non-working driver. In this case, hit Ctrl+Alt+F1, log in and run the command.
Another problem you may encounter are wrong LAN/WiFi/BT drivers, which may result in slow internet connections. As you didn't name the Ethernet or WiFi chip in your question, you should best look at the chip manufacturer's website and look for Linux drivers, or ask another question here, if you don't find any information about it.
Other than that, there often are only smaller problems, most of which can be resolved by the correct config or driver. Basically, ThinkPads most often run pretty well with Ubuntu.