The limited maximum aperture won't be too big a problem, but the limited focal length will be.
The upper end of both of those lenses is 16mm, which is (on the Nikon DX format, which I'm assuming because of the SB600) equivalent to 24mm on a 35mm (full-frame) camera. That's a focal length (field of view, perspective) that requires a certain amount of skill to take people pictures; you need to keep your subject away from the corners and short edges (that would be the left and right edges when the camera is in landscape orientation) in order to avoid visibly distorting them. Getting much wider is a matter of including more of the environment, since you really can't move the people out of the center square of the 24mm (16mm) field of view. 8mm (12mm equivalent) or 11mm (a hair wider than 16mm equivalent) won't let you get more people in unless you are willing to let them get pretty weird-looking; it's only non-special-effect use would be to capture the environment as well as the people.
You will very likely find that focal lengths below about 14mm aren't going to see a whole lot of use unless you are shooting architecture or landscapes. Both of these lenses would be great for either application (and the Tokina is an especially good lens for the money). But you're probably going to find that it's the range from 16 to 20mm that is going to be your go-to range for groups in cramped quarters, and both of these lenses leave the cupboard bare in the 16-18mm range (assuming you'd switch to your 18-55 when you want narrower than 16mm). Two millimeters doesn't sound like a whole lot, but it's a huge hole for the purpose you've described.
For about the same price, you can get the Nikon AF-S DX 10-24mm f/3.5-4.5 G ED, which offers overlapping coverage with your kit lens (making lens swaps less likely) and goes wider than is really safe for people shots anyway. And there's also the AF Tokina 12-24mm f/4 AT-X Pro DX, which is a bargain at the price and, again, goes wider than you'll ever need for people shots. (The Tamron and Sigma offerings in this focal-length range are low-priced and well-built, but optically unimpressive.)