Nope. Android apps are, with one caveat, independent of any particular architecture, due to their Java/Dalvik base.

The only situation where anything developed on x86 would not also work on ARM is if you include native code via the NDK (which is not usually done except where you need to wring every last bit of performance out of the device), and that's just a matter of building the native code for all the platforms you intend the app to run on.

The platform used by the emulator image makes no difference to any of that, it just makes it a lot more practical to get usable speed out of it.