I'm not aware of a way to include an index in an app, but you can include sample data. Just create a directory called "samples" in your app and put the data files there.
yes its possible, to ship an index with a app you need to include indexes.conf file with below sample structure,
[demo_index] coldPath = $SPLUNK_DB\demo_index\colddb enableDataIntegrityControl = 0 enableTsidxReduction = 0 homePath = $SPLUNK_DB\demo_index\db maxTotalDataSizeMB = 512000 thawedPath = $SPLUNK_DB\demo_index\thaweddb
This doesn't ship an index itself, just the definition of an index. Also, it's against Best Practices to ship enabled index definitions.