No, because Typekit is not font management software; it is a library of fonts that you can sync to your desktop to use alongside the fonts that you have installed locally. This tutorial shows how it works:
You can't upload your other desktop fonts to Typekit. You'll continue to manage them locally in Font Book, Suitcase Fusion, or another font management software.
I hope that this helps; let me know if you have any other questions. Best,