This can be easily done with some logic gates (2 IC's):
I am using NAND's and AND's instead of OR's because the outputs of the LM3914 are active low. I found from another answer that the outputs are open-drain, so I added 100K resistors to all the inputs.
All inputs on the left come from the outputs of the correspondingly named LM3914 outputs.
If all LED's are off, the output of all three gates on the left will be enabled (NAND gate IC1A low, AND gates IC2A and IC2B high), and the output of the NAND gate (IC2A) will be low, keeping the transistor off.
If any LED is on, the output of its corresponding NAND or AND gate will be disabled, and the output of the NAND gate IC1C will be high, turning on the transistor.
There is a special case for LED2-4, which will be blinking. I added a diode D1, two resistors R11 and R12, and a capacitor C1 to form what is essentially a retriggerable one-shot. While any of the inputs to IC1A are cycling on and off, it keeps the input to the IC1C low and its output high, keeping the transistor on. IC1B is being used as an inverter, since the gate was spare.
This shows a simulation of the timer circuit using Circuit Lab. The input to the inverter is kept above the minimum logic high-level of 2v while the input is toggling:
I have not shown the power connections or other pin numbers, but they are available from any datasheet for the parts. You could also use other logic families, such as CD4000.
I realize it really looks like I should be using an OR gate instead of an AND. As mentioned earlier, it is all because the outputs of the LM3914 are active low. It turns out an AND gate is equivalent to an OR gate that has both inverted inputs and output:
Follow the truth table through for each gate if you don't believe me. So the inverted outputs of the LM3914 match up perfectly with the inverted inputs of the "OR", and the inverted output of the "OR" matches up perfectly with the inputs of the next OR.
Holding the P-channel MOSFET closed (gate at 5V) will use hardly any power. It is basically the same as holding an N-channel MOSFET gate at 0V.
(See http://www.vishay.com/docs/91076/91076.pdf for a p-channel version of the IRF530 - same gate-source leakage current of +-100nA max)
To prevent powering the LED array via CLK or DAT you will need to either drive them low or set them to high-impedence when the MOSFET is off. Since CLK and DAT are both outputs, simply driving low is fine.
Note: This does not apply to your circuit here, but for inputs you can use a tristate buffer like the 74LVC1T45 or similar to prevent powering via signal pins... See FTDI (FT232RL) powers itself through RX/TX lines for the solution I used.
Alternative solution with existing parts
Actually, you could just move the N-channel MOSFET to the low side and drive CLK and DAT to 5V when you want to turn the LEDs off and go to sleep. That would address the problem in your first idea.
You can use the flashing bar display circuit shown in the LM3914 datasheet (figure 20). To have multiple flashing LEDs in dot mode you just have to add a diode between the timing capacitor and each output that you want to flash.