You can specify a a style that will run thoughout the editor... I do this to get the bulk of the text to look as close as possible to what it will look like on the live site. While I have not styled heading tags specifically, I have defined a style to use throughout the editor.
I simply created a new style sheet with one style and use it in the "class" selector for your editor.
My CSS sheet looks like this:
/* CSS Document */
font-family: verdana, arial, Geneva, "Trebuchet MS", "Lucida Grande";
So, now - even when I use heading 1, it DOES keep the font I supplied in my editor class.