Initial current in an RL circuit
Yes, you should consider that the initial current is V/2R, as inductors behave as short circuits in the steady state.

However, without doing any calculations, there are many things that tell me your answer is incorrect:


The dimension for your current is Voltage/Inductance,
which is wrong, should be voltage/resistance. 
The dimension of your exponent is R*t, which should be dimensionless, and it is
not.
When t goes to infinity, according to your answer, the current goes to zero. By the same 
logic that allowed you to determine that the initial current before the switch is flipped is V/2R, what should be the current after a long time has passed after the switch is closed?


HINT: Your voltage V is constant. What is the Laplace transform of a constant? You have V(s). Also, what is the Laplace transform of a derivative \$\large \frac{df}{dt}\$ ? Are you sure it's just \$s\cdot F(s)\$?