If I turn off iCloud backups for an app, will it affect it?
Welcome to Ask Different.
Your question can't be answered properly because it depends on the app your referencing.
Some apps need real-time access to the data they store in your iCloud or they won't work properly; some don't. Some apps will function fine without this access and some won't even start-up.
I recommend that if you're not sure, contact the developer of the app and ask them. You can also turn off iCloud and then check the app, too.