Do double reciprocal plot (1/Vo versus 1/[S]) work the same way as an IC50 plot and an enzyme kinetic plot?

The kind of plot would vary depending on the question you are trying to answer.

If you are working with inhibitors, you could use IC50 to determine the concentration of the inhibitor required to reduce the drug response by half. This will help you determine the effectiveness of your inhibitor. On the other hand, calculating the EC50 would be more appropriate if you trying to understand your drug potency associated with an enzymatic reaction, in which case, the EC50 will measure the concentration of a drug inducing its half-maximal response. Both IC50 and/or EC50 values are concentration dependent (based on the drug or inhibitor) and requires generating a dose-response curve. 

Finally, a double reciprocal plot is useful in understanding the enzyme-drug interaction i.e. the affinity of a drug to the enzyme/receptor. This can aid in distinguishing the type of enzyme inhibition that’s occurring in your system i.e. competitive, non-competitive, and/or uncompetitive. In this case, you will be calculating the maximum rate of reaction (Vmax) and the associated the Michaelis constant, Km, which is numerically the equivalent of the substrate concentration at which the rate of reaction is half of Vmax.

The data obtained from a double reciprocal plot can be compared among different experiments with similar experimental conditions, since this exploits equilibrium constants that are intrinsic to the experiment. However, the IC50 and EC50 values can be difficult to compare across experiments with varying enzyme or drug concentration.