Does using XLR cables (double voltage output) mean I can use lower powered amplifiers?

The amplifier gains the voltage difference between the xlr positive and negative signals, not the voltage magnitude. Since the gain is the same whether RCA or XLR, the power drawn by the speakers does not change, even though the balanced input is a higher voltage. An amplifier has two transistors on the input: one gets the positive XLR signal (or the RCA signal) and the second gets the negative XLR signal (nothing from an RCA input). The output signal is fed back at a fraction of its voltage to the second transistor and the difference between the two is amplified.

No, it does not work like that.

All XLR systems do is provide DIFFERENTIAL signals. This reduces noise considerably but does not change the gain and/or power transfer.

Below is a VERY simplistic explanation. The detail is much more complex but this is to give a very basic idea:

In an RCA cable (or any NON differential system), if you were to feed 2 volts of signal, typically it would be 2 volts on one cable and 0 volts on the other. If there was some noise of say 200 mV, then you may get 2.2 volts and still 0 volts, hence totally passing the noise to the amplifier.

In a differential amplifier, the same voltage will appear in both the cables as 3 volts and 5 volts (difference of 2 volts). With the noise, BOTH the terminals would be raised to 3.2 volts and 5.2 volts. Since the system works on the DIFFERENCE of the voltages, ie, 5.2 - 3.2 = 2 volts, your noise gets eliminated to a negligible amount.

Hence the much better noise rejection of an XLR differential system

Paul McGowan claims that tube amps can't be balanced.

+1 @cakyol

MC, you should change your avatar to a little knitted black and white bear with pins stuck in it…