Not necessarily, as I see it.
There is a range of coolant temperature over which the temperature gauge on the dash will not change when the coolant temperature changes.
As this diagram shows, if the coolant temperature is around 93 degrees (above the "(3)" on the bottom), a change in temperature to, say, 88 or 98, won't result in a change in the position of the pointer.
If the coolant temperature is running around 86 degrees (just where the line changes from sloped upward to horizontal, then if the coolant temperature goes up, the gauge remains the same, but if the coolant temperature goes down, the gauge pointer will move down as well.
The idea behind this is that the coolant temperature will change as driving conditions change, but as long as it remains, in this case, between roughly 85 and 100 C, the gauge doesn't change. That's considered the "normal" range. It's only if the temperature is outside that range when the gauge pointer will move away from the "normal" position.
What I believe is happening in your case is that the old thermostat was keeping the coolant temperature more-or-less in the area where the gauge response (in the diagram) is flat, whereas with the new thermostat, which we believe operates some 7 degrees F lower, the coolant temperature might be on the top end of the sloped part of the response line.
With either thermostat the ECT sensor still reacts any change in coolant temperature when the engine is in fuel cut, but the dashboard gauge reflects the change only with the new thermostat installed.
(I think we're on the same page here, and it's semantics -- how we describe the responses -- that might differ.)