On iOS, it is possible, but not guaranteed. I have managed to get ~6ms (22050 sampling rate, 128 samples buffer size) in my iOS app which does real-time processing of speech input. Take a look at Novocaine (https://github.com/alexbw/novocaine) - which provides a nice encapsulation of Audio Units and makes programming easier.
However, keep in mind that even if you request a particular buffer size, at run time iOS may decide to send larger buffers at longer intervals (=> higher latency) based on resource constraints. For example, if you have requested a buffer size of 128 (~6ms), you MAY end up getting 256 size buffers at 12ms instead. Your app has to take this into account and handle the buffer accordingly.
On Android, unfortunately, low-latency round-trip audio is a much bigger problem. This is because latency is driven by a host of device/manufacturer driven factors like hardware/driver level buffers and these vary from device to device. You can find a discussion of this long-standing Android handicap here: https://code.google.com/p/android/issues/detail?id=3434
My suggestion would be to ignore Android for now, and implement/validate your signal processing algorithms on an iOS device. Later, you can consider porting them to Android.