You do not need "drawing skills" to use Illustrator!
Just like you don't need "drawing skills" to use Photoshop.
The main benefit of using illustrator vs photoshop is that illustrator creates vector graphics. This means you can scale the images as large as you want or as small as you want and there will be no 'jagginess' because vector graphics aren't made from pixels.
Some things are best done in Photoshop, and some things are best done in Illustrator.
I have 0 drawing skills but work with illustrator almost every day. Like you, I used photoshop exclusively and didn't really understand illustrator. After learning to use it, however, I use it just as much as photoshop. It is a very valuable tool to know, and I'm sure you will learn to love it.
I would highly recommend that you master the pen tool as soon as possible. The way I learned the pen tool, was to place a background image of the Queen of Hearts from a deck of cards, and recreate it by tracing it using only the pen tool. After that everything else is easy.