Is that even possible?
I made an archive, validated & pushed it to itunes connect and I got a mail saying:
Invalid Deployment Target - Apps built with Swift must have a Deployment Target of 7.0 or later.
I get that swift is not supported on iOS 6 but since extensions are not either, doing this should be possible no?
The containing app itself is still entirely written in Objective-C.
I'm aware that extensions are available only on iOS 8.
Extension is a new feature in iOS 8 and it does not support iOS 7 and below. See https://developer.apple.com/library/ios/documentation/General/Conceptual/ExtensibilityPG/index.html#//apple_ref/doc/uid/TP40014214-CH20-SW1
Your app extension is written in swift. And Swift only support iOS 7+. See Swift with iOS 5 deployment target
So the answer is not possible. It also doesn't matter if your project is written in objective-c because of the above reasons.
Updated: it's probably good to just follow the instruction from iTunes connect to get your app approved.