Are there any drawbacks to cooking with limp celery? Crisp celery is important for salads and other recipes calling for raw celery, but what about when the celery is to be cooked, such as in a soup or stew? Celery loses its crispness when cooked so it doesn't seem to matter, but would I be missing something if I cook with limp celery?

I'm aware of how to revive limp celery to crispness from this question (How to keep celery crisp?) but it takes a few hours, and that question only addresses how to crispify it for raw uses, not whether it's necessary for cooking.
There's limp and then there's limp. As the celery ages, it will get more and more limp (and more bitter), and eventually neither delicious nor safe. If you're sweating the celery and it's a little less than crudité crisp it should be fine. Just sample it first to make sure it's not too bitter.