Why yes! Yes you can!!
So as I neared the end of a package of celery purchased at my local grocery store, I trimmed the base a bit and put it into a small vase. I watched as new leaves started to sprout out and grow. Based upon what I was seeing in the vase, it seemed to be working. How cool is this?!
The celery is the short one to the left in the picture (taken May 3rd). On the right is green onion - also part of the experiment. I'll tell you about that a bit at the end. For now it's all about the celery. ;)