I recall buying the Playmates Enterprise D in about 1992/93 (for $40.00 - my 10-year-old self got a little help from my stepbrother on that one), and I seem to remember it coming with two battery doors - one with an attached display stand, and one without.
Unless this was added to later batches of the model and I somehow acquired it, I'd say the early Playmates "D" did, in fact, have a display stand.
Regarding the Romulan Warbird: I had that one too, and I agree: the details were light. There was a single included "decal," the Romulan Empire symbol that went on the upper portion of the "beak." And it did do the lights and sounds thing: the engines' inner grills lit up blue and the available sounds were impulse, cloak, and, IIRC, two disruptor sounds.