Yes, you probably can get it "working", but you will not have the current control, microsteppeing and other features of the modern drivers. Also, You are operating the motor shield at the edge of its current specification and the L293 driver chip drops over 2.5 volts at 600mA so your motors will see only 9.5V.
My recommendation is to order the better drivers and junk the L293 based shield. The A4988 and DRV8825 drivers are available for less money (than Pololu) on Ebay. I linked the Pololu pages because they have lots of information on the use of the drivers.