I understand how localForage works in unison with a browser, but am less certain how it would interact as a part of a hybrid iPad app. There is no browser, per se, to store data in so I'm wondering if using localForage will still allow my data to be available offline.
So are you familiar with what a 'Hybrid app' is?
Not to be an a-hole about but a hybrid app, by definition is a 'web view' in a wrapper. Cordova, trigger.io etc are all basically doing the same thing. Taking the native browser ( IOS and Android ) and wrapping it in the context of an 'app'
thats the short version, you can read a lot more about it online, anyhow to answer you question about localforage..
LocalForage is a 'shim' meaning its uses what ever the platform will support, so for IOS below 9 ( I think ) it will use SQLLite and over IOS 9 and above it will use indexDB. With Android and crosswalk it will use indexDB ( unless otherwise selected )
Now for devices that do not support one of the other it will fallback to localstorage but that is limited due to the total size of storage