Will a skin unlock also unlock the hero at the same time?

Skin unlocks do not unlock the hero. The heroes must be unlocked separately.

However, you can unlock a skin without having unlocked the hero first - for example there is a Limited Edition Skin for a hero and you don't have that hero unlocked yet but you don't want to miss the skin, simply unlock the skin, and then later unlock that hero you will see that you have that Limited Edition skin ready to go!