Yes. As idioms, both can mean "to be alert and quick." I think "look sharp!" is more common in the USA. Either that, or I just use it more often. ;)

im kye

chiken

"Sharp's the word!" means: If you need to find one word to describe it, the word has to be "sharp". Thus: Sharp's the word. = Sharp is the word which can say it all, which can summarise all.