Connecting to a Bluetooth device from iOS, no MFi
That line is referring to standard profiles supported natively by ios devices, such as HFP or A2DP. If you build a headset device that does HFP, the iphone will be able to connect to it and route your call to the headset without the headset being part of MFi.
If you want to write an app that does other things with bluetooth, inlcuding FTP, you would have to use MFi.
If a bluetooth device is not in the MFi program, could an iPhone at least discover the device?
Yes you can discover - pair and in connect also as long as both the device supports the standard profiles (like HFP, A2DP, PAN etc) , to do these you dont need MFi.
MFi is only needed if you want your app to talk to your accessory - which will be possible only over non standard profile (like a protocol / over the SPP profile) in which case you will have to build your device as per MFi.
Would I be able to pair my iOS device with a custom bluetooth device if it gets MFI license?
You must apply for MFi program just to get access to the Bluetooth APIs that you need. There is no other way without bypassing Apple's legal requirements.
Existing bluetooth device and Apple MFI
If your app is not going to app store, you can try using the private framework called BlueToothManager. I haven't worked with it but it can help you.
The MFI compatible devices are registered with Apple and communicate with a Bluetooth Profile registered with Apple. That particular protocol string (Eg. com.apple.ps1) will be given by the MFI device manufacturer, which you will need to include in the info.plist file.
Iphone bluetooth connected to a non-MFI device
For connecting to non-registered-MFI device you have to jail-break your iPhone and then you can connect it by writing code in C.
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