This article is from the Dr. Pepper FAQ, by Christopher Flaherty with numerous contributions by others.
The simple answer: No.
The more complex answer: No, they didn't.
The long answer: Why something like this generates attention, as
opposed to genuine problems (like say, the lack of a decent rail
system, a shortage of affordable housing, and an electoral process
that leaves a lot to be desired, to name a few) is beyond me. Here
are the facts:
-- In early 2002, the Dr Pepper company issued a promotional can which
had a picture of the Statue of Liberty on it, not the Empire State
Building (and how the Empire State Building could be "patriotic" I'll
never know). You can see a picture of that can here:
-- That same can had printed on it the exact phrase "One
-- The full text of the Pledge of Allegiance was never printed on this
can in the first place, so nothing was omitted from it--unless you
count the use of that excerpt as omitting something, in which case
over 90% of the Pledge was omitted, not just the words "under God".
So, while it is technically true that this can did not have the words
"under God" on it, it would be equally true to say that it didn't have
a million more words from the English language on it as well.
-- As it turns out, the words "under God" were not even part of the
Pledge of Allegiance when it was written in 1892 by Francis Bellamy, a
Baptist minister. Those two words were added in 1954 by Congress to
deliberately inject religion into public schools in an attempt to
somehow show the United States as being better than so-called
communist countries at the time. Two years later in 1956, Congress
changed the national motto of the U.S. from "E Pluribus Unum" (Latin
for "Out of many, one") to "In God We Trust," for similar reasons.
In any event, it seems that the above facts morphed via the Internet
into the above rumor, and have been circulated by enough people to the
point where it now qualifies as a bona fide urban legend. Apparently,
there are even people out there who are willing to "boycott" Dr Pepper
because of the lack of the aforementioned two words in question on
that can, and that makes me wonder: are those same people going to
boycott every other soda pop on sale now too? Because I don't see the
words "under God" on any soda can in stores right now, do you?
Oh, well. More Dr Pepper for me, I guess.