Could it be bad if I don't get a tooth crown replaced immediately?

Very possibly. A crown is usually replaced because decay has gotten under the crown. Delaying replacement will lead to greater amount of decay and tooth destruction plus the possibility of needing root canal therapy and a post.
When to replace. It depends on why it needs to be replaced. If there is decay or damage then it should be done asap to prevent further damage and possible loss. If it is esthetic than no it doesn't. If it is causing gum issues it would be a good idea to prevent any irreversible issues. If there is pain i would also do it asap to prevent need of root canal or worse. See a qualified dentist.