The simple answer is, of course, no.  You can't copy something that doesn't really exist.  But, I assume, what you mean to ask is, "could a hacker trick the network into believing that he has more bitcoins to spend than he actually does"?  The answer to that questions a "yes, sort-of".  However, the two known ways of doing so are; 1)already known and well considered and 2) extremely difficult to pull off.  Those two attack vectors are the Double Spend attack and a 51% hashrate attack.  Considering that Bitcoin now rings in at 300 Petaflops continuously dedicated to securing against a 51% attack, the only realistic vector is the Double Spend.  And that is effectively negated simply by waiting for multiple confirmations.