He could have, but it would have been a long shot. He lacked the name recognition that Bush had and wasn't prepared for a national campaign, as evidenced by his missteps with the tank and the debate question about his wife. Not to mention that voters were generally happy with the state of the nation at the time, which made his case harder to make.
Strong economy+popular incumbent make a Dukakis win extremely unlikely.
See Richard Nixon in 1960 and Al Gore in 2000
Although you're right that satisfaction with the status quo doesn't always mean a win for the incumbent party, I would argue that Bush was a much stronger candidate than Nixon in 1960 or Gore in 2000. In 1960, Nixon refused to let Ike campaign for him until the last few days before the election, and Gore similarly refused to appear with Clinton in 2000. Bush, meanwhile, used Reagan's support to his advantage and made a convincing case that he would continue those policies. Not to mention that he was also more aggressive at attacking the opposition than Nixon and Gore were.
After the conventions, he led by 17 points in the polls and then lost by margin, that was never outperformed since then (53.4% of the vote and 426 electoral votes).
That was after the Democratic convention. Prior to the conventions, the polls had him even with Bush, and after the Republican convention Bush took the lead. (See
this video, for instance.)
