If she did not use either EAD or AP, then she is still F1.
Some other questions:
1. Since she can apply for CPT, why she can not apply for OPT?
2. If when she graduate next May, she still did not receive approved EAD, then what is her status then? Will she need to change to H4?
3. What do you mean 'don't bother'?
Thank you very much!