For me, strobes are much better than continuous lighting. Continuous lighting gave me some good results, but it was a lot more work and I had to be much more careful. The lights were hot as heck, hard to work around, always had to shoot on a tripod, aperture had to be wide open and the shutter was almost too slow. Strobes is a different story. Much more control, not hot, rarely use a tripod, can light a much larger area with much less equipment.
As far as a flash per se, I never use my flash in the studio at all. There's always a wireless trigger on the hotshoe anyway, so it can't even pop up. The only reason to use it with continuous lights is to fill a little where the continuous lighting isn't cutting it. I never did with continuous lighting. It seemed to mess things up more than it helped.
If you have good continuous lighting, you shouldn't ever need it.