Just tried sending it a request while ‘side button’ sleep mode and it woke up perfectly immediately. It just doesn’t go back into that mode without pressing the side button, so I really see no reason you can’t blank the display.
At this time the ability to have the device go to sleep isn’t currently available. 
I just received a Square Terminal and this is a really annoying behaviour, to the point I might just return the terminal.
As has already been mentioned, this behaviour makes no sense as if you press the side button to turn the screen off it works perfectly fine. Everybody’s just asking for the device to obey the Display Off setting to enter the same mode. Turning the display off doesn’t have to mean entering a sleep mode. Why is there even a menu option for turning the display off automatically if it’s never obeyed? It’s just a bewildering design choice that makes no sense to me.