If I have a group of Arduinos connected via I2C, can one Arduino cause the rest to freeze?
There are a number of places in the standard Wire library where the code goes into a tight loop waiting for an interrupt to occur. If that is missed for some reason, it will loop indefinitely.

By removing power from one of your devices you may be introducing electrical conditions that prevent the I2C messages from being transmitted properly (possibly just noise). Alternatively the device may parasitically power up from the SDA/SCL data and then behave in unpredictable ways. It is probably unwise to do this.

There is an alternative I2C master library at http://dsscircuits.com/articles/arduino-i2c-master-library which does not hang (I believe it times out instead).