As a Front-End Developer is it all right if I don't learn Photoshop but Illustrator instead?

While I agree with Illustrator being more intuitive, I would suggest you learn at the very least, the basics of Photoshop. It's not that hard in comparison to Illustrator so learning the basics would be best. Most companies use Photoshop over Illustrator when designing mock-ups but it will vary by company.

Hell ya. I am by no means a designer and that is often a huge struggle of mine. I usually have to lean on designers for help.. Illustrator is from my understanding best used to create vector art, I have designer friends that swear by Illustrator. I've used it from time to time but I find myself going back and forth from Illustrator to Photoshop. But I'm sure Photoshop could still serve some use to you in conditioning your assets for production.

I'd be willing to bet that Illustrator will serve you better. Any high end photographs should be (in my opinion) touched up by a skilled photographer. What you're going to be most interested in, I believe, is vector graphics. And while Photoshop can do vector graphics, Illustrator is all about vector graphics.