How to identify when a pulsed rf supply is active
AM demodulation consists of a diode detector and this will work just fine for getting the envelope of the signal i.e. the pulse envelope. Don't use a bridge rectifier these are notoriously slow and won't rectify properly with anything much faster than a few kHz. Use a BAS16 or IN4148 followed by a resistor to 0V and a capacitor in parallel.

You haven't stated the amplitude of the RF so a few extra precautions may be needed.