It depends on your definition of 'turn off'. If you disconnect Vdd from the supply then pull it down to 0V, the PIC will be off and all the I/O pins will effectively be pulled low via their upper internal protection diodes. If you don't pull Vdd down, if any pin has more than about 2V feeding into it from any source, the MCU will probably continue to run (to some extent - normal operation *NOT* guaranteed), powered from its inputs via their protection diodes.
If you need all pins Hi-Z, then you *NEED* that /MCLR pin available so you can hold the PIC in Reset (unless you monitor another input and set all other pins as input when its asserted in code).
If all I/Os low with Vdd pulled down doesn't meet your requirements, you'll either have to be more efficient in your pin usage, multiplexing some uses to free up a pin, or you'll need to go up to a 28 pin part with similar features.