The modeling light on monolights are not intended for general room illumination. Typically, one does not leave the modeling lights on all the time. It probably wouldn't hurt them, aside from shortening their life, but the existing room lights are much more efficient at general lighting.
With any type of room lighting you will have to deal with the light color and the white balance. If you do your own post-production editing, you can adjust the white balance after the shoot.
Most monolights do have an optical trigger that can be triggered by any flash. One thing to consider is how your built-in flash will help or hurt the other strobe lighting. It could be used as "on-camera fill", or modified in some way so as not to interfere with your other lights.
There are other ways to trigger strobes, such as; wired, using a PC cable (you will have to purchase an inexpensive hot shoe adapter), or a wireless radio type of trigger system, where one unit mounts on the camera, and the other unit(s) trigger the strobes, or using the Nikon CLS (using certain models of Nikon speed lights). Another way is to set a speedlight to operate as a "slave" and trigger it with your built-in flash. This is actually not the CLS, but it still works. I have a SB-910 that I use that way, and I think it works great.