If you are trying to determine to 1%, that's only 1 part in 100, so 16 bit is 600x better than that.
How fast do you need a reading? What frequency is the input? The built in analog updates at just over 1ms, but that isn't fast enough to give very good resolution. If your input is 60hz, you would only get about 15 samples per wave. I suspect that taking samples over many waves would give you enough data to make a really good estimate of true RMS. Easy to test. May be good enough.
Might also be able to full wave rectify and filter (with a cap) and then measure the DC. Would have to account for the diode drop. Might work. Not sure about accuracy, but it wouldn't be hard to test either.
Barring either of those, then no, BRX doesn't have a method to accurately measure RMS.