I don't have the lens and have never used one so my comments come from shooting in somewhat low-light situations. Here is a SOOC photo taken yesterday immediately prior to the Worship service. It was a test shot to check the exposure--it is completely unedited except for forum resizing.
I was in aperture priority--no exposure compensation was used. ISO 2500, Nikon 70-200mm f/2.8 lens shot at f/5, 1/80" shutter speed. I'd say the lighting was not overly bright by any means but a little brighter than it looks here. Most of the images taken were shot at @180-190mm.
By zooming in, the camera meters a different area. Even though the lighting didn't change, by zooming in, I wound up having adjust my exposure by -0.3 stop. I even opened up to f/4, and although I underexposed the remainder of the images, the shutter speed slowed down to 1/30". Like I said, when you zoom in or out, the camera is metering a different area. I was surprised I needed to use ISO to 2500, but I really didn't want my shutter speeds to be too slow. 1/30" was definitely slow enough for the remainder of the images.
I've also photographed my local high school's drama productions. When I first started, I used a Sigma 70-210 f/3.5-4.5 lens. It handled the lighting okay, but when I took my Nikon 55-200mm f/4.5-5.6 DX lens, most of the time it hunted. I believe you should be fine to shoot with the lens you mentioned because it is an f/4 lens and not one with a variable aperture.
If the lighting winds up being too dim, you will have the option to switch to live view and focus manually.