I don't think there is that much danger with freshly washed celery consumed immediately, but when it sits in a salad for a day or two, you can start growing a culture. Having said that, however, remember the problems traced back to the cilantro used in a chain of Tex-Mex restaurants and there was bacterial contamination in the water with which it was sprayed in the field or something.
The old southern term for what you do with your celery is "roping" to remove the strings.