Without the two diodes the circuit functions as a "collector bend" detector, with the diodes a "base bend" detector. Whats this all about you say?. For a demodulator to function at all there needs to be some non-linearity in its circuit. The simplest demod is a single diode, when signal goes +ve it conducts, if the signal goes -ve it does not. This is a gross form of non linearity. The theory behind the original circuit is that the transistor should only be conducting pA of base current and micro amps of collector current so if the input signal goes +v it conducts more and if the signal goes negative , the transistor cuts off. When you remove the diodes the transistor goes into saturation, i.e. its conducting as much as it can, so any +ve signal will be ignored, but a -ve signal will bring it out of saturation and the collector voltage will rise, i.e. it will work as a demodulator. Rather then the the diodes, it would be better to take the base via a 100K to the centre tap of a pot, so you can adjust the pot so the collector voltage JUST fall from Vcc with no signal input.
Frank