A deployment target means that the should work on devices running that deployment target iOS version (or later). (So, if your deployment target was 4.3 and the device is running an iOS version of 4.3 or greater, you should be fine.) The fact that you used Xcode 5 and the iOS 7 SDK will not affect this. The only limitation is that we cannot use the latest compiler to build for iOS versions prior to 4.3 and/or the first or second generation hardware.
Clearly this assumes that you didn't accidentally reference any classes or methods that require later iOS version (or if you decided to avail yourself of new features, that you put in runtime checks to only use those new methods/features if they were available). Try running your app on an iOS 6.0 simulator to confirm compatibility with iOS 6. (Note, Xcode 5 no longer includes the simulators prior to iOS 6.0, so if you really want to test against earlier versions, such as iOS 5.0 or 4.3, you might just want to get your hands on some old device with that older iOS version.)
I mention getting an older device, because compatibility with the old iOS version is not enough. You want to ensure your app can run on that hardware (e.g. doesn't require more than the 4th gen 256mb of memory, cellular, etc.). You really should find yourself physical hardware with older iOS versions upon which you can test your app.