Can I use Serial Port Profile (SPP) to communicate with iOS devices over Bluetooth Low Energy (v4.0) without the need for MFi Chip?
If you're designing something from scratch (rather than trying to interface to an existing SPP-enabled device), there is a possible solution.
Laird Technologies make a Bluetooth Low Energy Module (BL600), which can be loaded with a virtual serial port application. This creates a service which is similar to the SPP; at the remote end it can just be treated as a plain serial port (albeit rather low speed). You could roll your own service to do something similar on other devices.
It's not the most elegant solution, but seems to work okay, and far easier than trying to get MFi certification.