Is it possible, once I've converted the circuit diagram into its Laplace equivalent, to replace a current source which is in parallel with, in this case, a resistor and inductor by the usual V=IR method considering I treat the R in the equation as a combination of the impedances from both the resistor and the inductor?
Yes, you can convert the circuit diagram by replacing the impedance in parallel to the current source even after converting to the Laplace domain( This is because Laplace transform is simply domain transformation for simplification of calculation and has nothing to do with the circuit itself).
But, the way you've transformed the circuit isn't correct(on the L.H.S voltage source, R.H.S. is fine), since the voltages across the L.H.S and R.H.S circuit aren't the same which you can verify yourself.
Alternatively, if you really want to convert to a voltage source, first convert the 3 ohm connected to the ground as two 6 ohm resistors connected in parallel to the ground and then you can use one 6 ohm for converting current to voltage source like you've done above.