I want to write a lipoly powered arduino device that can be launched from sleep mode by pressing a certain key that is connected to ground. Usually, when no in sleep mode I enable the internal pull-up resistor for a definite level. But when in sleep mode, I assume this would drain to much power and hence I want to avoid it. Is it sufficient to just wait for a pin-change interrupt on the same port pin without the internal or an additional external pull-up resistor?
You must not leave CMOS inputs floating. This will increase power consumption, and as a worst result may damage the device. Use an external pull-up if you feel that the internal pull-up passes too much current.
Tutorial from University of South Florida https://www.youtube.com/watch?v=HiAbxSO_9nU
Internal pull-up resistor does not drain too much current. Only leakage in nA range. It is correct to use pull up, in your case, as this is what it is designed to do. As Ignacio Vazquez-Abrams, do not leave input pin open.
MCU are designed to do the precise action you mentioned, to wake up on pin change as in mass produced wrist watch and TV remote controller. On remote, MCU sleeps until key pressed. On watch, it wake on timer 1 second) and key change.