It depends on what you're testing exactly, but as a general principle I'd have to say yes, it's worth it. Apple change quite a lot under the hood during iOS version changes and it's hard to know whether, for example, an internal bug fix or optimisation from iOS6 -> iOS7 might affect your test outcomes.
If your project supports iOS6, you really need to have your tests run on iOS6.
To get tests that run on iOS6, create a test target and select 'OCUnit' from the drop-down (XCTest is iOS7 only), or you can use something like GHUnit which also supports iOS6.
The mocking/injection thing sounds interesting but I don't think it's any replacement for properly running your tests on genuine iOS6 devices.