Does iTunes Home Sharing transfer in-app purchases?
Firstly, you must bear in mind that each In-App Purchase is uniquely associated with an Apple ID and that there are different In-App Purchase types:


Consumable - You need to purchase these items every time you want them, and you can't download them again for free.
Non-Consumable - You purchase these items one time, and you can transfer them to multiple devices authorized with the same iTunes Store account.
Non-renewing Subscriptions - You can purchase these items again after the subscription period ends.
Auto-Renewable Subscriptions - You can purchase these items with different renewal periods.


There are, therefore, differences in the way the availability of the product is handled.  

As stated on Apple's iTunes Store: About In-App Purchases:


  You can't sync or transfer non-renewing subscriptions and consumable In-App Purchase to another iOS device or Mac. You can transfer non-consumable In-App Purchases and auto-renewable subscriptions to another iOS device or Mac authorized with your iTunes Store account. For example, if you transfer a game from an iPhone to an iPod touch, only the game levels will sync, and the extra ammo and experience points won't transfer.