Yes, you can route MDF. It will take an edge shape, dadoe, or rabbit quite nicely.

Can you put a router edge on MDF?

yeah, you can certainly route MDF. the edge can be a bit fuzzy and will require some extra sanding as you put on the first coat or 2 of paint since it will make it swell up a bit. Its very doable, just takes that extra care.

Is MDF hard on router bits?

A standard bit will do the job just fine,, MDF is Hard on router bits , I would not suggest you use the high price carbide up-spiral bit just pickup SOME standard router bits..