Can we use the phrase 'Hit the bricks' at the context of asking people to work hard?
As LessPop points out it is generally a reference to leaving.
It could be construed to mean "go work hard," but it would have to be highly contrived:
I can imagine a boss telling his underling the details of a job. Giving him a bunch of warnings about the quality expected, etc. And, then following it up with "Now, go hit the bricks!".
The meaning would still be: get out of here and start working. But, the get working hard would probably be implied.
Again, it is a highly contrived example to shoehorn the phrase into the meaning you asked for.
Some better idioms:
Put your nose to the grindstone.
Put your back into it.
Go work your heart out.