How well does Ubuntu work with a dual CPU computer?

Yes, Ubuntu is more than capable of using the Xeon PC you want to buy and detect all CPUs (Physical and Threads). It can also detect, as far as I have tested 4 sockets (4 CPUs) but the kernel version that Ubuntu uses can detect even more. For this case I would suggest the 64 Bit version so you can max out on the performance benefit of all CPUs. Of course, this will also depend on the video editing tools you use. If they are not compatible with running multiple processors, then you will not see much improvement. I for one use for example Handbrake which takes advantage of multiple processors but at the end it all depends on:

• Using 64 Bit version of Ubuntu for performance benefits when using multiple processors
• Using a video editing app that can actually use multiple processors when doing any processing work.

Recommend reading this questions I just found:

Is Ubuntu optimized for multicore CPUs?

For better performance should I install 32-bit or 64-bit?

Understanding machine config, multiprocessor or multi-core or both?

And others found in the tag multi-core