Can I get hot water faster if I were to leave the fawcett open all the way?

Question

Edit "... if I were to open the fawcett all the way?"

Answer 1

Of course.

Answer 2

If you mean when you open the faucet to get hot water, yes, the wider open the faucet the faster the water flows through the pipe, and the sooner it would reach the faucet.  If you mean if you were to leave the faucet on, then no, you would very shortly run out of hot water.  

Answer 3

That's "faucet" actually but never mind.  The water in the pipes from the water heater has cooled, not surprisingly so you have to get it out of the pipes first before you can get hot water.