Based on my experience with runners,
yes they can eat out of a chick feeder - some ducklings may need a shallow open tray the first day or two, but mine were using the feeder right away
I am brooding them indoors, in a very large tub. At about 4 days old, we had a swim in a cake pan in about an inch of water, and dried off with the dry towel that was their bedding. At about 7 days old, we had a swim in two inches of water in a 90 degree F tub, for about 3 minutes, then went right back into the clean, dry, 90 degree brooder to dry. I watched them closely. One seemed unable to preen herself dry, so I scooped her up and dried her with a washcloth. at 10 days old, we did the bathtub routine again, 3 to 5 minutes, and again I helped dry three who were soaked and did not seem to be able to handle preening. The other eight were fine. I watched until everyone was mostly dry.
If you don't have time to spend with them after, just wait.
Without supervision, they must have their feathers, and have them properly oiled (
) and I would (as I am sure you will) give them a test run or two, and watch for whether they are able to get into and out of the water easily or not.