In a word, no.
Since the Iowa Caucuses started to matter in 1976 until 2004, there were 6 races in which both the Democratic caucuses and New Hamphire primary were contested. The Republicans had 5 such Republican contests.
In 1976, Jimmy Carter and Gerald Ford won both states. Carter repeated the feat in 1980. Al Gore and John Kerry did it in 2000 and 2004.
Split decisions, however, have been just as common. In 1984 and 1988, Gary Hart and Michael Dukakis won New Hampshire after losing Iowa. Ronald Reagan and George H.W. Bush did the same in 1980 and 1988. So did Pat Buchanan in 1996 and John McCain in 2000.
New Hampshire has been especially likely to contradict Iowa's choices after especially close caucuses. Remove the blowout caucuses on the Democratic side (none of the Republican caucuses in that period were really blowouts) in 1976, 1980, 1984, and 2000 from the calculations, and split decisions are actually more common than back-to-back wins.
As we saw above, the 1988 Democratic race falls in the split decision category. So do the Republican races of 1980, 1988, 1996, and 2000. Only the Democratic race of 2004 and the Republican race in 1976 saw back-to-back wins for a single candidate.
So, which event is a better predictor of the nominee? Well, Walter Mondale won Iowa and survived a New Hampshire loss to take the nomination. On the other hand, Michael Dukakis suffered a third place finish in Iowa before a New Hampshire win helped carry him to the nomination. The evidence on the Republican side is no more conclusive. Reagan and George H.W. Bush lost Iowa in 1980 and 1988 but won New Hampshire. Bob Dole and George W. Bush did the opposite in 1996 and 2000.
The points is, this has happened before and will probably happen again. The race goes on.