Yes, It can be done by using Sheet library option.
"When you insert a live data sheet into your story, the current selections of the app are saved with the sheet. every time you view this sheet in your story, these selection will be applied and will show updated story"
Please refer to the sample attachment (Snapshot and Sheet Library story methods attached)
Just tested with functionality with Qlik Sense 3.1 SR3 (when ever data get reloaded/refreshed then Story will get updated by automatically just make sure to use Sheet library option.)
I you wish to go for pixel perfect /advance report design formatting and then email distribution then you can go ahead for Nprinting 17+
Qliksense_247082.qvf 176.0 K
Only solution i think you can do is embed a sheet in story and that should change based on your data load or selections. Something like define all your content in a seperate sheets so that you can embed them in story. There will be extra sheets but this is the only way.
Other option would be to wait until next release 4.0 (june/July 2017) which might have this option.