What is the slowest shutter speed I can use for Nikon 70-200mm 2.8 with VR?

I'm shooting a nikon 7000 70-200mm 2.8 VR. Of course depends on how fast subject is moving, but just handholding what is slowest shutter i could normally use to get a sharp picture? Since there's a crop factor, should I make up for that, and shoot even faster, such as 1/250 or more, when i'm zoomed all the way out?
Also… I have a 2x teleconverter with the 70-200 2.8, which would make it a 600mm with crop. So the slowest shutter I could use for this be 1/600? Or would i be able to get a sharp photo handheld at 1/500 with VR?

I guess I don't quite understand. Do you want to freeze action? A moving object can be frozen nicely at 1/1000 but 1/500 also works well depending on the subject's speed, as you mentioned. For hummer wings I find 1/800 and 1/1000 work very well.

By the way a crop factor has nothing what ever to do with shutter speed / sharp image. Any sensor regardless of size will capture what ever is presented to it by aperture and shutter speed so forget about the crop because it doesn't matter.

The above shutter speeds are all dependent on available light and ISO. For example, I did this on a rather dark, rainy day, under a patio roof at 1/800, ISO-3200, with a Canon 28-200 lens fully zoomed to 200mm. My f/stop was 5.6

Assuming your subject isn't moving, the rule of thumb for shutter speed is 1/(focal length) for full frame cameras (FX in Nikon lingo). For a crop sensor camera (DX), minimum shutter speed is 1/(focal length x 1.5) sec. This is assuming you are hand holding your camera. If using a tripod, shoot at any shutter speed you desire.
With the newer high pixel sensors (e.g. D7000, D800) this rule of thumb gets blown out the window, so for your DX camera it's probably 1/(focal length x 2).

With VR, you can shoot 2 to 4 stops slower (depends on the vintage of VR). Lets say VR gives you 3 stops advantage. At 200mm, lets say you need to shoot at 1/400 seconds without VR. With VR, you should be able to shoot at 1/50 seconds. You actually need to go out and experiment. Shoot with VR off and see what shutter speed you can shoot at and still get a crisp shot. Turn VR on and repeat experiment. Some people are steadier, some are more shaky. Camera holding technique is important.