The administrative organ informs the higher authorities of the administrative acts by means of notification. Does the notice have legal effect?

First, you can't write to your superiors by notice. The notice belongs to the lower level, and sometimes it can be used for writing, but not for the higher level. So I'm a little confused when you say that you can inform your superiors by notification.

Second, the criterion for judging whether a party can bring an administrative lawsuit is that the administrative act has affected its interests and does not fall within the scope of not bringing an administrative lawsuit as stipulated by law. If your notice is an internal administrative act and does not affect the rights and interests of the opposite party, you cannot bring an administrative lawsuit. On the contrary, if it affects the interests of the relative person and does not fall within the scope of administrative litigation prohibited by law, then it can be prosecuted.