Different strobes treat the modeling light in different ways. Some turn it off and then it comes back on when the unit is fully recycled, but others leave it on all the time and others leave this to your choice.
However, the modeling light is not going to affect your shots unless you are doing something really special. The average strobe fires in 1/500th to 1/3200th of second and that is what the exposure is based on. Since you normally will be shooting at the camera's sync speed (1/60th, 1/125th or 1/250th) for most dSLRs then it is impossible for the modeling light to affect the photo.
Typically you'll be shooting at f8 and one of the above sync speeds, but would need to be shooting a 1/8th to expose a light bulb at f8 properly).
Example: if you wanted ambient light to affect the photo, then you can drag the shutter. When shooting in bars where there are neon signs, I might drag the shutter at 1/8th to properly expose the Neon sign, but the flash exposes the model.