Yes, you can check in and explain the situation. A Disney ADR is just as much a reservation as one at any other restaurant. When they give you a time, they are telling you that you will be seated at or near that time, and most often that's exactly what happens. That's why, if you decide to skip the ADR, you can't just say, "well, I didn't actually have a reservation, I was just supposed to show up and wait for the next available table." Most restaurants outside of Disney (at least the ones we go to) handle reservations the same way as Disney - very few will set aside an actual table for a specific party. The difference is that when someone makes a reservation in their hometown, going to the restaurant is their main focus and they usually know how long it will take to get there. At Disney, people may have FastPasses that encroach on their time, the distances and time it takes to get to the restaurant are often underestimated, modes of transportation can be overcrowded, people may linger at their meals for any number of reasons, etc.
If it's any help, we've made more than 50 trips to Disney over the course of 35 years and have never waited as long as an hour for an ADR - last time our party of six was seated slightly ahead of time at 'Ohana. I can remember only 3 times ('Ohana, Le Cellier and Coral Reef) when we waited more than 15-20 minutes, which I consider to be a reasonable wait time at Disney.