That should not be an problem. Each user can provide their own spreadsheet ID to the script, however, usage of the script at the same time by different users may cause some issues...
Perhaps the best thing to do is to include a unique ID for each row, you can then edit the update script to find the correct id. You might want to consider using this method:
Because you have date numbers, you will need to understand how to write your SQL statement for these:
When using my CRUD methods, it may be best to return all the records to your app, and to then select/query the records you want in the app, working with lists to amend/update, and to then return them to the google sheet.