Is it possible to reverse (as in flip vertically) a single character (in my case the '~' character) inside a line of text WITHOUT converting the text to outlines? As in it's still a character, it just happens to be reveresed?
You can rotate a character - which may or may not work for you. There's no way to "flip" a character though.
To rotate, simply select the character and alter the option fields in the Character Panel. You may need to choose
Show Options from the Character Panel Menu first.
Here, I've adjusted the baseline shift as well to bring the rotated character back down to the baseline of the other characters.
In Illustrator CC, you can click the Touch Type Tool button on the Character Panel to alter text with click-dragging. It still doesn't allow you to "flip" the character, but you can more easily adjust rotation, placement, and size of individual characters this way.
These are pretty much the only transformation you can make to a single character in a line of live type.