That is not a question that we can not readily or authoritatively respond to here since the font in question was not licensed from Adobe.
The American Typewriter fonts bundled with MacOS are indeed visible to and usable within Adobe applications. In fact, I did try creating an InDesign document using all six styles of that font on my Mac system. I also successfully exported PDF/X-4 from InDesign and the fonts embedded without a problem.
However, all that means is that Apple (or the foundry from which Apple licenses the font) have not put any physical security in place to prevent font embedding within PDF (or EPS or PostScript). That having been said, you would need to obtain the actual license for the font from Apple to determine if they or their vendor has any restrictions against such commercial use.
If you had licensed the font from Adobe, the answer would have been that you could embed the fonts and use them as you described. You could not embed them in an HTML stream or with an application program for dynamic use (such as with an iOS or Android application). But as part of a static logo, you would be good to go.
You need to see if Apple has its font licenses on its website to ascertain what their restrictions, if any, are. If the license is not on their website, you may need to contact Apple's legal department.
- Dov