Not recommended. At 1.1A each Darlington driver will be dissipating a significant amount of power (>1W) due to its internal saturation voltage (the VCE(SAT) number in the datasheet on page 6). This will cause the chip to be destroyed. Yes, it says "up to 1.5A for each Darlington" but that is marketing-speak and assumes you are aggressively heat-sinking the device, and does not say anything about 1.5A for ALL 4 Darlington's at the same time (no way!)
Never trust a number on the front page of a datasheet
I'd stick with the discrete transistors at these current levels.
I'm not sure what you mean by "TTL logic isn't compatible with Arduino", indeed it is and the three devices you picked out can be driven from an Arduino.
The Gadget Shield
: accelerometer, RGB LED, IR transmit/receive, speaker, microphone, light sensor, potentiometer, pushbuttons