Does the north bridge/south bridge affect the performance of a processor?

Northbridge handles the processor, mem, L2 cache, and PCI bus + AGP.
Southbridge controls I/O (usb, serial, etc).

A better N/S chipset does make a difference for a mobo's highest possible potential.
IF you have a processor that has more features (HT, EE, faster bus speed, etc) and is not supported by your mobo's N/S, then you will be missing out on those features or there might be compatability issues.

Yep. Buy a motherboard with a sis chipset then one with an nforce4 chipset and you will be surpised in the difference. CPUs are not the only factor in speed.

So is the performance impact great enough that I should pay a $20 premium to get an nForce4 Ultra over a VIA K8T890?

Defo go nFORCE

Oh god yes. Via was still a little bit faster than an nforce3 but all the new nforce4 boards should be way faster. BTW that is if you are going to build an AMD system. I do not do a lot of intel builds so I am not sure what is best for them ATM.

If you need help pickin out a board id also be happy to help. It will be an asus though :-p