Nope.
That is, it depends on your viewpoint.
The ship that Uhura and Chekov visited was said to the USS Enterprise, CVN-65. In the real world, the vessel that bears that name and registry looks exactly like in that drawing, and Picard's ready room wall also had a relief that looked like this. Also, in the real world, this look is unique to CVN-65, as the funny-looking command tower or "island" features a distinct square radar array (for a radar that has long since been abandoned).
However, during the filming of the movie, the Enterprise was not at port and could not be filmed. Instead, the non-nuclear USS Ranger, CV-61, was dressed up as the Enterprise.
Since the external differences between the real Ranger and the real Enterprise are in fact rather minimal and superficial (essentially limited to that "island" which, as said, only looks like that because nobody has bothered to completely remove a bit of outdated hardware), it would by no means be difficult to claim one of the following:
1) In the Trek universe, CVN-65 looked like the real Ranger in the 1980s but was refitted to look like the real Enterprise later on, and is remembered in her final guise.
2) In the Trek universe, CVN-65 looked like the real Enterprise originally, but was refitted to look like the real Ranger in the 1980s, yet is usually remembered in her original guise.
3) In the Trek universe, there were at least two nuclear carriers named Enterprise. The one registered CVN-65 looked like the real Ranger, and was in existence in the 1980s. The other, carrying some other registry such as CVN-52 or CVN-96, looked like the real Enterprise and was in existence before or after the ship that Chekov and Uhura visited. This other vessel is the one that is better remembered, possibly because she participated in the Vietnam War or the Eugenics War or WWIII while the Trek CVN-65 only served in the Cold War and never actually fought any real battles.
Take your pick or make your own bit of pseudohistory. The fact is, a total of three different aircraft carriers supposedly named Enterprise have been shown in Star Trek (the two discussed above, plus the old WWII carrier CV-6 which is visible as a drawing on the recreation deck in ST:TMP). Of these, we only know that the one that at one point looked like the real Ranger had the registry CVN-65 as visible on some ST4 props; the Trek registries for the other two vessels have not been clearly shown or told.
That is, unless you can somehow zoom in on Archer's artwork and see the numbers "65" on the bow of the flight deck. But if you can't do that in an actual episode, but only manage it if you use backstage sources, does it count?
Timo Saloniemi