Who needs to join the Apple MFi program?
The company that plans to market the end product that carries the MiFi certification is responsible for obtaining that certification.
There’s no expectation that every component on the BOM be manufactured in house.  You have to submit product designs, plans, specifications and even packaging before you begin manufacturing.  Then you must submit samples for both mechanical and electrical testing to ensure that it complies.
Do you need MiFi certification?
No.  You can develop products that have apps that provide their functionality be available via the App Store and not be MiFi certified.  One good example would be Bose.  They market headphones as “Apple Version” or “Android Version” with an app in the App store and there’s no MiFi certification.  Notice that the quoted text is not “Made for iPhone” (or similar).  To say that, would require MiFi certification.
Regarding your specific situation, the FAQ provides answers:

I want to develop an accessory that communicates with an Apple device using only Bluetooth Low Energy. Do I need to join the MFi Program?
No. Accessories which connect to an Apple device using only Bluetooth Low Energy/BLE/Bluetooth 4.0 or standard Bluetooth profiles supported by iOS are not part of the MFi Program.



I want to develop an iOS app that communicates with an MFi accessory. Do I need to join the MFi Program?
No. iOS app developers do not need to join the MFi Program. Everything app developers need is in the External Accessory Framework, which is provided in the iOS SDK.