Fast switching ULN2003's GND Pins
switching the ULN2003's GND (Pin 8)with a transistor at 1KHz. 


No,that will not work.

At the moment that you 'switch' the ground off you have lost the reference against which the inputs switch. In other words: your whole ULN2003 is floating and you have no idea how the inputs will react to that, but my educated guess is bad. 

Much better if you would switch the 24DC supply with a high-side switch.