Nano BLE 33 as programmer for ATmega328P?

Can I use the "Arduino Nano BLE 33" (ARM Cortex-M4), to program an ATmega328P (AVR) via Arduino IDE? If not, why?

I had some problems with it a while back, but I tried again recently and I seem to recall that it worked (though I might be misremembering because I was also testing with the Nano Every at the time). So I recommend you to just wire it up and see what happens.

You should use the latest version of the ArduinoISP sketch because there are one or two relevant fixes done recently that happened after the release and so aren't available via the Arduino IDE's Tools > Examples menu or Arduino Web Editor. You can get it here:

If you're powering the ATmega328P at 5 V, be very careful not to expose the 3.3 V Nano 33 BLE to 5 V.