No, it does not affect the app store submission. XCTest is also not supported as far as I know if your app still runs on older versions of iOS.
You will need to switch "at some point", because Xcode 6, which might be released as a beta in the next few weeks, probably will not support OCUnit. You may not be able to run your unit tests at all soon unless you upgrade.
But until then, there is no pressing need to upgrade. When you're ready to do it, just commit all your changes to git/etc so you can roll back if it goes wrong, then click the "convert to XCTest" button. It should just work... if it doesn't, post here with your specific problem.
As a general rule, I would not rush to adopt any new features in Xcode. There tend to be bugs and sometimes Apple abandons new technology a year after adopting it. But XCTest has been the default for a year now, and I haven't heard any complaints (except for bugs in the early days), so it's safe to switch.