The answer to this is pretty easy. It depends on what you want to do as a career. (If you don't know what you want to do, check out this List of Illustration Careers.) I can't comment on every single career possibility out there, but most illustration jobs fit into one of two major categories:
Do you want to do concept art, animation, or otherwise work on video games and movies?
Then yes, you need to learn digital art. It's the industry standard. Sorry, there's just no way around this. In addition to learning digital painting, you may need to learn 3D modeling and animation programs, depending on what job you're aiming for.
Do you want to illustrate for books, magazines, children's products, tabletop games and the fantasy market?
Then the answer is no, you don't necessarily need to do digital art. Both digital and traditional mediums are welcome in these fields. In fact, I'd say both publishing and editorial lean towards a traditional look. If you can achieve a traditional look using digital painting, or using a hybrid method, that's fine too. Art directors don't usually care what medium you use, as long as it looks good.
Many artists work in hybrid methods, for example sketching roughs digitally, then painting the final traditionally. (For a good example, see Julie Downing's hybrid picture book illustrations.) Other artists learn both methods so they can use digital for assignments with short deadlines, traditional for those with longer deadlines.
Even if you prefer to work traditionally, I would still encourage you to learn your way around Photoshop. You're going to need to devise a method of working that is quick and allows for you to make changes. Clients will be asking for revisions, and your answer can't be, "sorry, I can't, it's traditional" or "well I guess I have to paint the whole thing all over again." If you can scan/photograph your physical painting, you can make those revisions in Photoshop as long as you know some tricks.
I hope that clears some things up!