Negative. Being struck with water pressure is what opens the detergent door. That’s why it’s sprung like a mousetrap and so easy to jostle open accidentally. You can take the door and dispenser apart if you like and you will find no electronics in there. Also, if you look carefully at the upper wash arm you’ll see it has one nozzle on the tip that points outwards, not up. That’s the one that makes the stream designed to hit and open the detergent door.

Of course, the dishwasher’s program determines when to blast it at full pressure to pop it open. So it is “timed” in that sense.