I am working with someone on a data logger based on an MSP430. Since it operates on battery power, we want the device to use as little power as possible. We are planning to use this chip (FT201X) to interface the device with USB in the next revision. When the chip is running, it draws considerable current, and when it is in standby mode, the current drawn (125µA) is still more than several other components on the board, so it seems like it would decrease battery life nontrivially, which isn't desirable since the chip doesn't do anything when it's not connected to USB. Most of the time the device will not be plugged in to USB. The device has its own I2C bus connected only to the MSP430, so disabling the bus might work, but would add hardware to handle the pull-ups.
My question is whether it is safe or not to leave the FT201X unpowered (that is, only powered by USB, and unpowered by the circuit) for normal use and only let it power up when USB is supplying power. I'm concerned that the I2C lines, which each will have a 1K pull-up resistor to 3.3V, might damage the chip when it has no power. The data sheet says that the inputs have an internal resistance of 75K, but the SDA might be the problem. Am I right in assuming that this is a bad idea?
Additionally, what other options might I have? Is it possible that I could power VCCIO but not VCC? That might be my favorite option if it's possible. I suppose other options include connecting the pull-ups to FETs or, I suppose, powering the chip always. Are there any better ways?