How can I see if ADR (Adaptive Data Rate) is working with my end device (MultiTech's mDot module)?

But not the “The next backend release will make it work for devices that don’t receive downlink from the application layer”, right? If it is, please see ADR - not what I expected.

look at the “trace” of the downlink messages in the gateway view

Indeed, nice; see this screenshot of the trace of the ADR downlink:

The Things Network Console

(Though I didn’t see it when the node does not respond to SF9 in RX2, and TTN then repeats the ADR in SF12.)