Can I use a 3.3v tolerant microcontroller to drive IR leds that require 5v with a darlington array?
You can drive the ULN2003a with 3.3V outputs- they don’t put any voltage onto the driving circuit.

Of course if you mess up the circuit or the grounding your chances of ruining the Pi are much higher than if you use 3.3V only.

You need series resistors for the LEDs and you should make sure that the maximum total current can be supplied by the 5V supply. Since they don’t tend to be grossly overrated it’s unlikely an extra 800mA will be acceptable. Also, in your comment you mention 7 ohms, which would yield several hundred mA and quickly destroy the LEDs and the ULN2003.

If you use an auxiliary supply the ground must be common. Connect the supply ground to the ULN2003 ground directly and that junction to the Pi ground.

If you’re making a PCB there are nifty SOT-23 MOSFETs  that have very low voltage drop at 100mA and can be driven directly from the Pi.