Since the typeface install is an issue with the OS, I would think that it has to be installed separately. AE simply looks at what fonts are installed on the system to compile its' list. The Collect Files command will give the option to list the fonts use, but does nothing in terms of collecting or installing. Here's the word from Adobe:
I'm sure this has a lot to do with typeface licensing. You can't just send off a licensed typeface to anyone - unless it's a free or open source typeface, that's illegal. That said, I'm sure it's done all the time. In fact, I've had clients send me typefaces which I didn't own, and needed for a project, only to find that it's a $250. font set.