Running 32u4 at 3.3V

[uberben]

I have cut the VCC jumper on my 32u4 breakout board. I then tested for continuity across these pads with my cheap analog continuity meter and there is still a significant buzz sound (though not nearly as loud as the when I touch the probes to each other. I then went to measure the resistance across the jumper and the resistance was too high to register on my meter.

I then plugged it into my computer and see that it is no longer enumerating, as expected as the chip should not be getting power. However, I measured a few pins on the ISP header and elsewhere and noticed several pins were floating around 1-1.5V. Is this normal? Should I be concered by this when I hook up up my external 3.3V source?

[adafruit_support_bill]

Be careful using your continuity tester on electronic circuits. If it is not a low-voltage current-limited tester it could damage your circuit.
You can't draw any conclusions from the voltages on the floating pins. Go ahead and connect the power source.

[adafruit_support_mike]

Most integrated circuits have things called 'clamping diodes' on all the inputs. They're basically diodes that are reverse-biased under normal operating conditions, but start to conduct if the input moves too far past the supply rails.

In most cases, taking a pin's input more than .6v above the Vcc pin will make the upper diode start working, and taking the input more than .6v below GND will make the lower diode start working. The upper diode is connected to the chip's internal Vcc rail, so you can actually power a chip through any of its I/O pins when the VCC pin is disconnected. I won't say it's a good idea -- the clamping diodes aren't made to handle a lot of current -- but it's physically possible.

When you connect your 3.3v supply, the VCC pin will take over again. Just remember to keep the input signals below 3.3v.