Would not be a problem as long as the device conencted via the Darlington Array can tolerate being switched on an off when you are downloading a program to teh PICAXE.
For example, having an LED permanently (via resistor) connected to Out0 is normally not a safety issue but having a motor pulsing or starting and stopping may be an issue.
BUT
please reconfirm the chip you are using.
If it is a ULN2803 chip. Well that is the chip number given on your schematic,
pin 9 should be connected to ground (0 volts) and pin 10 is tied to the supply for the free wheeling diodes
However, if it is a ULN2003 (with only 7 "channels" as shown) then your connections are right
Think you are using the ULN2003 as the basis of your pinout