The phrase they would be devastated refers to the emotional condition of someone in the wake of some shocking news or grief.
As an example, consider this dialog:
Where were you last night?
I was in jail.
In jail? What happened?
I was at a bar and got into a fight.
Have you told your parents?
Oh, no. They would be devastated.
Essentially, the person is saying that he wants to spare his parents from the emotional shock they'd get from the bad news. Another (figurative) way the character might say that last line could be:
Oh, no. They would disown me if they knew I was arrested.
NOAD defines the word as:
devastate (verb) cause (someone) severe and overwhelming shock or grief : she was devastated by the loss of Damian.
I'm not sure who "would be devastated" (or why) in the short excerpt you've provided, but I can venture a guess. It could mean that his wife and kids enjoy their quiet life in the country, and they'd be devastated if he obtained some high-level cabinet post. However, I don't think that's too likely. Because it's on the heels of the remark, "Too queer," it could mean:
And wouldn't his wife and children be devastated to learn that he was a homosexual?
but there's not enough context provided here to be sure.