I can’t draw at all, so will that hurt my chances of succeeding as a designer?

you will only miss the chance of using illustration within your concepts. but you still can use typography, colors, lines and simple shapes.

Actually there is no one can not draw at all, i am sure you have a basic foundation of drawing or sketching, you need sketching more to express your ideas.

you can develop your sketching skills by drawing courses to cover all aspects of drawing: Anatomy and landscape and push your talent in: perspective, composition, balance ...etc

If you can't draw, no matter, but you imagination, your devotion, your passion would be the key to success in designing field. 

Try to learn draw and practice. This will be advantage in many designing tasks. 

not necessary at all. to become a great designer u need the passion and the mind to see the things around. observe others and be updated 

Not at all, You still have the chance of being a successful designer. It is the Idea within your mind and translate it thru your computer works is the most important thing as a Designer. But It is a big plus having the skill to draw.

Succeeding as a designer has no relation to drawing. To succeed as a designer you need to have the passion and determination to be a successful designer. Knowledge is your first weapon plus experimentation and getting inspiration from various resources. Be attentive to your environment and listen to clients carefully to catch the details.

If you can draw you have a talent; but if you can design, that's a profession.

No this will not affect your design career on the other hand if you have drawing talent it will give you a huge push in your career