Of course not, that's absurd. If anything, he was one of the most experienced presidents when it came to politics. He was a two-term Congressman, a two-time Senate candidate, RNC chair, head of the CIA, and vice president. His father was also a Senator; though that doesn't count much for him personally, it shows that he was raised in a politically conscious family.
While Reagan's coattails and the general good state of the country certainly helped HW win in 1988, it was far from the only thing that helped him, and he had to fight in order to win. Dukakis was a weak candidate who made a number of costly mistakes (the tank, the debate question from Bernie Shaw, etc.) and whose record on crime, the environment, and economic issues was vulnerable.
I don't think New World Order Guy was particularly incompetent, but he obviously sucked at the politics game and only won his first term because everybody thought Willie Horton was on the ballot.
Not true, Dukakis made a number of missteps that hurt him almost as much as Willie Horton. The tank ride was heavily ridiculed both by Republicans and the news media, and his horrendous answer to Bernie Shaw's death penalty question during the debates made him look insensitive. IIRC, Bush actually took the lead in the polls after the GOP convention, several weeks before the Willie Horton ad first aired.
As for the NWO thing, the "new world order" HW was referring to was the one created by the fall of the Soviet Union, one where the US was the only superpower.