Can a comma ever proceed ending quotation mark?

According to Webster's Third New International Dictionary:

"In American usage printers usually place a period or comma inside closing quotation marks whether it belongs logically to the quoted matter or to the whole sentence or context.... But when a logical or exact distinction is desired in specialized work in which clarity is more important than usual (as in this dictionary), a period or comma cn be placed outside quotation marks when it belongs not in the quoted matter but to a larger unit containing the quoted matter."

Since your example is not a case in which clarity is more important than usual, I think the comma should be inside the quotation marks: Jimmy's got bad "morning breath," because he didn't brush his teeth before bed.

Here is an instance when the commas and the period should be outside of the quotation marks:

In first-order theories in which equality is definable, we can define a special type of existential quantifier "(E! x)A", which means intuitively "there is one and only one x such that A", or simply "there is a unique x such that A". ---The Logical Foundations of Mathematics, by William S. Hatcher

Yes, usually in BrE you would put the comma after the inverted commas:

1. Jimmy's got bad "morning breath", because he didn't brush his teeth before going to bed.

Though I probably wouldn't use a comma there anyway. (I'm also doubtful as to whether brushing your teeth before going to bed prevents 'morning breath'.)

MrP

This is an unfortunate example because we don't normally use a comma before a "because clause", i.e., when it precedes a "because clause". Supposing a comma were needed there, it would always go outside of the scare quotes, in my opinion. Quoted speech is another case. "Americans handle it like this," he said. "Even if they have 'morning breath'," she added.

I doubt the last sentence would be written: "Even if they have 'morning breath,'" she added.
It may even depend on which style manual you are following.

CJ