Correct, there is no exposed heating element and therefore no drying cycle. Reasonable time is subjective, so that is hard to answer straight up. In your scenario however, yes, the dishes would be dry by 7am. I noticed in the operating manual that using the Sanitized feature/option heats the water up to a higher temp and hence speeds up the drying time - I have found that to be true. Also, when the DW finishes up its cleaning cycle, you can open the door for about 15 min or so and the dishes dry relatively well.
Hope this helps.