Hey Kev -
Lot of good answers here that all support what I would tell you - ambient room light shouldn't affect your shot because your Bees will over power it. 99% of the time I shoot with the room lights on because my D100 has trouble focusing. In fact, when I do evening shoots, I usually turn on some halogen torchierie lights just so I can focus on the model. Only time I don't use ambient light (and use modeling lights only) is when I'm shooting against a black background and want it to look jet black.
All that said ... for a change of pace, use the ambient light as an additional light source!
For many of my images, I incorporate the ambient light as part of my shot. If you spend a little time learning about light temperature (Kelvin) and how it affects the color of an image, you can expand your lighting arsenal with many different types of lights. I have 3 Alien Bees and 4 Norman strobes, but I regularly use incandescent, flourescent, halogen, tungston, mercury vapor and daylight in my shots (mostly as background lights). You'll need to master the art of rear sync and dragging the shutter, but it's something that can be learned with a few hours of practice.
In this example image of Jennifer, I used one Alien Bee to light her face ... but rather than letting the background drop off to black, I used several incandescent lights in the background to give the image a golden look.