Yes you can. Air gaps are required by some codes but not all. The way you install the drain without the air gap is to loop the hose over the DW and attach it to the underside of the counter. It must be secured so it will stay in place and not kink. In other words, fasten in in more than one location under the counter. You may have to get a little creative to provide something to attach the hangers to, but it can be done. I've never used an air gap in my home in 35 years, and never have had a problem. The hose attaches to the sink drain the same way with or without an air gap. In the disposal if you have one or a special tail piece ahead of the trap if you do not have a disposal.