When you look into the viewfinder. The lens is always at it's max aperture. It only stops down when you press the shutter button to snap the photo. Unless you press the DOF preview button. This stops down the lens aperture so that you can preview the DOF. (DOF is controlled mainly with the aperture of the lens, if you didn't know).
So yes, because the aperture gets smaller, the viewfinder gets darker. But if you let your eye adjust to it...you may be able to tell that you can see a deeper DOF in the viewfinder. Just how dark it gets, depends on the aperture that the camera is set to. If you have it set for F22...then the viewfinder will get so dark, you won't be able to see. But if you set it to F8 or F11...you should be able to still see. It doesn't get darker when you are set to the max aperture (F3.5 to F5.6) because the lens is already at the max.
It doesn't help that most DSLR cameras have tiny viewfinders compared to 35mm film SLR cameras. Back when we shot film, the DOF preview was easier to use.
With digital, you might as well take a test shot and review the image on the LCD.