Can I darken an oak table & chairs with no sanding?

You can, but if your chairs are used on a daily basis, you might want to use a palm sander and regular stain, so it soaks in. Gel stain just sits on the top, and does not penetrate.

I stained oak cabinets with gel stain, without sanding.

1. If you don't want to sand your chairs, at least give a light, but good scrub with steel wool and a deglosser/liquid sandpaper. Do NOT skip this step.
2. Wipe off the residue (dirt etc.) with a lightly water dampened textured cloth or towel.
3. Let dry thoroughly.
4. Apply stain with a glove or sock over a vinyl glove.
5. I recommend adding a top coat like Stays Clear (but follow the directions on your type of stain). I skipped this, and although it has held up well overall, there are a couple of spots that need touching up.

I think it depends on how shiny your furniture is. The color will have to be able to permeate whatever finish is on it. I used black paste shoe polish on an oak colored entertainment center and it has darkened it very well. I didn't want it black, but just wanted to take the "yellow" out of the original finish. Try your gel stain on a small unseen area first.

I did minimal sanding when I refinished my casual dining set and I did use gel stain on the table top and chairs as well as chalk paint on the legs. Look here:

http://www.hometalk.com/diy/kitchen-dining/kitchen-dining-furniture/you-inspired-me-to-do-it-i-tackled-refinishing-my-casual-dining-set-8141238