The signal from the discone that ends up at the coax conector are delayed more than the signal from a vertical element on top of it, something like 1/8 to 1/4 wave out of phase. With a vertical that has a coil in the middle, that are a phase twisting coil usually for a 1/2 wave top part to phase match to a 1/4 wave bottom part, will create havoc to direction patterns and gain if allowed to operate in the same frequency range as the discone.
But as the discone in itself have a skewed direction pattern above 600MHz, that could make it loose 10dB-20dB of signal, it might actually improve signal strength with that collinear vertical element but will also have a negative impact at lower frequencies. It will be impossible to predict how it will perform. So as usual with antennas, experimenting and practical tests are the way to go.
/Ubbe