I need to eliminate the MOSFET drive circuit from my PCB by replacing uln2004 or uln2803, should I still keep the back EMF diode across the dc motor?
motor supply 5V current 70mA
If the load has inductance, you must use freewheeling diode. Otherwise, you will probably damage the supply and/or MOSFET when breaking the current.
You cannot change current of an inductor instantly. So you have to provide a path for inductor to “discharge itself” safely. If inductor does not have that path, it will reverse the voltage as high as needed to keep the current flowing. You can see this in light switches as a blue light (arc) when you try to turn off the light.
Note that relays and motors have coils, and they should always have a freewheeling diode.
The ULN200x and ULN2803 have built-in diodes, all connected to a COM pin. Tie this pin to +VSUP, and you do not need external diodes.