I've created custom fields on a custom object in my org that came with Agile Accelerator. I want to know if there are any downsides to doing this. My largest fear would be updating the package and it deletes my custom fields and associated data. Could this happen?
No. Custom fields are separated from the packaged managed fields through their namespace, and these customizations will persist so long as the package is not uninstalled completely. There are no inherent downsides to adding custom fields on custom objects in managed packages. Your main concerns should be that validation rules and automations you add to a package may break the package's functionality.