Jimmy Carter was a nuclear engineer. But a lot of people didn't end up liking what he did. Some still say that he ruined the country. I'm not knowledgeable enough to know what he should have/have not done, but I know a lot of people that despise the man.
After stating that, I still would like to see more engineering types in leadership positions because engineers are more data driven. However, most engineers are too busy building things to run for office.
Out of character for a scientist? You mean, besides Werner Heisenberg, Freeman Dyson, Francis Collins, Richard Smalley, and Donald Knuth? This meme needs to die.
Nuclear Engineer? From his Wikipedia I wouldn't really categorize him as a scientist. It also says he was really religious, which is also out of character for a scientist.
Woodrow Wilson was an intellectual (though not a scientist) and he was president.
Keep in mind the president's cabinet members probably consist of many scientists and this is probably sufficient for advising and keeping the president knowledgeable on issues.
Woodrow Wilson was a disaster, and quite the anti-intellectual towards subjects that lent themselves towards one correct answer. Some quotes of his: "I don't let facts cloud my opinions". "The natural man despises mathematics". Also, his Treaty of Versaille was the main cause of WWII. I have no idea why he is revered as a president.
EDIT: After brushing up on a little ww2 history, it seems as though I've attributed too much blame to Wilson. He pushed a liberal approach towards Germany, the French delegation pushed for harsh reparations, and he lost out.
After stating that, I still would like to see more engineering types in leadership positions because engineers are more data driven. However, most engineers are too busy building things to run for office.