The answer is partially yes. There are three things to be considered to answer this question.
1. Whether Note 9 Spen will fit inside an note 8?
2 Does note 8 have the hardware to charge Spen?
3. Will the features other than Spen remote function will work?
1. I don't know the answer for he first question.
2. Note 8 can't charge the super capacitor inside Note 9 Spen, so the remote control function will not work.
3. The hardware for Spen in all the note lignups are identical. You can use any spen on any note device to write on the screen. The pressure sensitivity for each spen will be different but you can still use any Note 1 Spen on Note 9.
So if its just for writing on the screen any spen will work. But the remote control function will not work on note 8. Also I haven't tried inserting a note 8 oen into note 9.