Not really. It's on the dash in the second film also.
If HT are possibly encompassing the delorean for 1 and 2 then that makes sense. Either way, I would not count on that tiny accessory as a hint at what doc is coming. HT really don't care that much.
There are five versions of the car across the movies(Not counting interim stages, like the "wrapped up in the mine" version from the beginning of Pt3).
Technically, all versions are the same car, just at different points in time.
V1 is the one that both Einstein and Marty use to travel in time, powered both times by slugs of plutonium and makes the aforementioned two trips. Einstein travels one minute into the future, and Marty travels from 1985-Prime to 1955 Prime(Which instantly becomes 1955-B due to Marty's interference at Twin Pines Ranch).
V2 has the clock on the dash, no plutonium, a lighting hook on the top that hooks into the flux capacitor(But is left in 1955-B when the Delorean hits the cable), and makes two trips in time(That we know of): Marty travelling from 1955-b to 1985-B, and Doc travelling from 1985-B to 2015-Prime.
V3 is the hover-converted Mr.Fusion-powered version that Doc comes to 1985 to take Marty and Jennifer forward to 2015 in. It makes seven trips through time in Pt2(1: Doc travelling from 2015-Prime to get Marty and Jennifer, 2: Doc, Marty and Jennifer travelling back to 2015-Prime(Which, due to their interference becomes 2015-B), 3: Old Biff leaving 2015-B and travelling to 1955-B(Which becomes 1955-C due to the new presence of Old Biff), 4: Old Biff travelling back to 2015-B, 5: Doc, Marty and Jennifer travelling from 2015-B to 1985-C(Being the direct result of Old Biff's machinations in 1955-C), 6: Doc and Marty travelling to 1955-D(Which now has two Marty's, Two Doc's and two Biff's), and finally, 7: Doc being blasted from the air in 1955-D back to 1885-Prime by the lightning bolt(Which now becomes 1885-B because Doc is there with an anachronistic time machine from 1985).
As an aside, due to the ripple effect, the car itself(And the ability to travel in time), would have been lost forever if Marty and Doc hadn't quickly worked out how Old Biff had gotten the Almanac to young Biff. Doc would have been committed again(Or simply vanished), and with that, the Delorean would either have vanished, or just turned into a normal Delorean.
V4 is the car Marty travels from 1955-D to 1885-C in(This timeline now having Marty, and another Time Machine in addition to Doc, but which *could* result in Doc being shot). It is 70 years and 9 months older than the car he last travelled through time in, has new 1955 valve-technology electrical components to replace the fired microchip in the time circuits and 1955 wheel rims with whitewall tyres, and makes only one trip.
V5 is the car Marty uses to travel from 1885-D(Which is now the altered sequence of events where Doc *wasn't* shot, and Buford was arrested and jailed) and is almost exactly the same as V4 except the wheels have been removed and steel railroad wheels have been fitted, and the car has a steam/temperature gauge hooked up to the locomotive. Marty arrives back in 1985-D, where everything is the same as 1985-B except for Clayton/Shonash Ravine is now Eastwood Ravine.
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